Question 1

Three forces are in equilibrium: 1500 N, 3000 N, and 2500 N. Find the angles between their lines of action.

Accepted Answer

$\angle(1500 \mathrm{~N}, 2500 \mathrm{~N})=86^{\circ} 11^{\prime}, \angle(1500 \mathrm{~N}, 3000 \mathrm{~N})=123^{\circ} 45^{\prime}, \angle(2500 \mathrm{~N}, 3000 \mathrm{~N})=150^{\circ} 4^{\prime}$

Question 2

Fill in the missing parts of this table for triangle $A B C$.

Accepted Answer

$B=55^{\circ} 9^{\prime}, C=89^{\circ} 27^{\prime}, c=4.1$

Question 3

Two vectors of magnitude $A=346$ and $B=437$ are separated by an angle $\theta=19.4^{\circ}$. Find the resultant and the angle the resultant makes with vector $B$.

Accepted Answer

$772,8.56^{\circ}$

Question 4

Write the sine, cosine and tangent of $\theta$, where $\cos \theta=5 / 13$ and $\sin \theta$ is positive. Leave your answers in fractional or radical form.

Accepted Answer

The answer of Write the sine, cosine and tangent of...

Question 5

A triangular lot measures $257 \mathrm{~m}, 316 \mathrm{~m}$, and $177 \mathrm{~m}$ along its sides. Find the angles between the sides.

Accepted Answer

The answer of A triangular lot measures \(257 \mathrm{~m}, 316...

Question 6

Fill in the missing parts of this table for triangle $A B C$.

Accepted Answer

The answer of Fill in the missing parts of this...

Question 7

Solve the oblique triangle $A B C$ if $A=25.1^{\circ}, B=59.0^{\circ}$, and $b=3.53 \mathrm{~m}$.

Accepted Answer

The answer of Solve the oblique triangle $A B C$...

Question 8

A building is going to be $6.1 \mathrm{~m}$ wide. The roof will be supported by two $4.6-\mathrm{m}$-rafters. What is the angle at the roof peak?

Accepted Answer

The answer of A building is going to be \(6.1...

Question 9

Fill in the missing parts of this table for triangle $A B C$.

Accepted Answer

The answer of Fill in the missing parts of this...

Question 10

A building is going to be $7.10 \mathrm{~m}$ wide. The roof will be supported by two rafters, one $2.25 \mathrm{~m}$ long and the other $5.25 \mathrm{~m}$ long. What is the angle at the roof peak?

Accepted Answer

The answer of A building is going to be \(7.10...

Question 11

Evaluate $\sin^{2} 172^{\circ}-15 \cos^{2} 32^{\circ}$ to four significant digits.

Accepted Answer

The answer of Evaluate $\sin^{2} 172^{\circ}-15 \cos^{2} 32^{\circ}$ to four...

Question 12

Three circles are to be bored in a plate. The circle $A$ with a diameter $4.00 \mathrm{~cm}$ and the circle $B$ with a diameter $5.50 \mathrm{~cm}$ are tangent to the circle $C$ with a diameter $7.50 \mathrm{~cm}$. Determine the distance between the centre of circle $\mathrm{A}$ and the centre of circle $\mathrm{B}$.

Accepted Answer

The answer of Three circles are to be bored in...

Question 13

Evaluate, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\theta=\operatorname{arcsec} 12.02$.

Accepted Answer

The answer of Evaluate, to the nearest tenth of a...

Question 14

Vector $A$ has magnitude 10.1 while vector $B$ has magnitude 8.63. The angle between the vectors is $2.09 \mathrm{rad}$. Determine the magnitude $R$ of the resultant and the angle $\theta$ that the resultant makes with the vector $A$.

Accepted Answer

The answer of Vector $A$ has magnitude 10.1 while vector...

Question 15

Evaluate $\tan^{2} 17^{\circ}+\cos^{2} 17^{\circ}$ to four significant digits.

Accepted Answer

The answer of Evaluate $\tan^{2} 17^{\circ}+\cos^{2} 17^{\circ}$ to four significant...

Question 16

Solve the oblique triangle $A B C$ if $a=1.5, b=2.2$, and $c=1$.1.

Accepted Answer

The answer of Solve the oblique triangle $A B C$...

Question 17

In which quadrant will the terminal side of $\theta$ lie if $\theta=-235^{\circ}$ ?

Accepted Answer

The answer of In which quadrant will the terminal side...

Question 18

Write the sine, cosine, and tangent of $\theta$, where $\tan \theta=-4 / 5$ and $\theta$ is not in the fourth quadrant. Leave your answers in fractional or radical form.

Accepted Answer

The answer of Write the sine, cosine, and tangent of...

Question 19

Fill in the missing parts of this table for triangle $A B C$.

Accepted Answer

The answer of Fill in the missing parts of this...

Question 20

Two vectors of magnitude $A=144$ and $B=280$ are separated by an angle $\theta=59.8^{\circ}$. Find the resultant and the angle the resultant makes with vector $A$.

Accepted Answer

The answer of Two vectors of magnitude $A=144$ and $B=280$...

Exam 15: Oblique Triangles and Vectors

Three forces are in equilibrium: 1500 N, 3000 N, and 2500 N. Find the angles between their lines of action.

Fill in the missing parts of this table for triangle ABCA B CABC .

Two vectors of magnitude A=346A=346A=346 and B=437B=437B=437 are separated by an angle θ=19.4∘\theta=19.4^{\circ}θ=19.4∘ . Find the resultant and the angle the resultant makes with vector BBB .

Write the sine, cosine and tangent of θ\thetaθ , where cos⁡θ=5/13\cos \theta=5 / 13cosθ=5/13 and sin⁡θ\sin \thetasinθ is positive. Leave your answers in fractional or radical form.

A triangular lot measures 257 m,316 m257 \mathrm{~m}, 316 \mathrm{~m}257 m,316 m , and 177 m177 \mathrm{~m}177 m along its sides. Find the angles between the sides.

Fill in the missing parts of this table for triangle ABCA B CABC .

Solve the oblique triangle ABCA B CABC if A=25.1∘,B=59.0∘A=25.1^{\circ}, B=59.0^{\circ}A=25.1∘,B=59.0∘ , and b=3.53 mb=3.53 \mathrm{~m}b=3.53 m .

A building is going to be 6.1 m6.1 \mathrm{~m}6.1 m wide. The roof will be supported by two 4.6−m4.6-\mathrm{m}4.6−m -rafters. What is the angle at the roof peak?

Fill in the missing parts of this table for triangle ABCA B CABC .

A building is going to be 7.10 m7.10 \mathrm{~m}7.10 m wide. The roof will be supported by two rafters, one 2.25 m2.25 \mathrm{~m}2.25 m long and the other 5.25 m5.25 \mathrm{~m}5.25 m long. What is the angle at the roof peak?

Evaluate sin⁡2172∘−15cos⁡232∘\sin^{2} 172^{\circ}-15 \cos^{2} 32^{\circ}sin2172∘−15cos232∘ to four significant digits.

Evaluate, to the nearest tenth of a degree, all positive angles less than 360∘360^{\circ}360∘ where θ=arcsec⁡12.02\theta=\operatorname{arcsec} 12.02θ=arcsec12.02 .

Vector AAA has magnitude 10.1 while vector BBB has magnitude 8.63. The angle between the vectors is 2.09rad2.09 \mathrm{rad}2.09rad . Determine the magnitude RRR of the resultant and the angle θ\thetaθ that the resultant makes with the vector AAA .

Evaluate tan⁡217∘+cos⁡217∘\tan^{2} 17^{\circ}+\cos^{2} 17^{\circ}tan217∘+cos217∘ to four significant digits.

Solve the oblique triangle ABCA B CABC if a=1.5,b=2.2a=1.5, b=2.2a=1.5,b=2.2 , and c=1c=1c=1 .1.

In which quadrant will the terminal side of θ\thetaθ lie if θ=−235∘\theta=-235^{\circ}θ=−235∘ ?

Write the sine, cosine, and tangent of θ\thetaθ , where tan⁡θ=−4/5\tan \theta=-4 / 5tanθ=−4/5 and θ\thetaθ is not in the fourth quadrant. Leave your answers in fractional or radical form.

Fill in the missing parts of this table for triangle ABCA B CABC .

Two vectors of magnitude A=144A=144A=144 and B=280B=280B=280 are separated by an angle θ=59.8∘\theta=59.8^{\circ}θ=59.8∘ . Find the resultant and the angle the resultant makes with vector AAA .

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Filters

Fill in the missing parts of this table for triangle $A B C$ .

Two vectors of magnitude $A=346$ and $B=437$ are separated by an angle $\theta=19.4^{\circ}$ . Find the resultant and the angle the resultant makes with vector $B$ .

Write the sine, cosine and tangent of $\theta$ , where $\cos \theta=5 / 13$ and $\sin \theta$ is positive. Leave your answers in fractional or radical form.

A triangular lot measures $257 \mathrm{~m}, 316 \mathrm{~m}$ , and $177 \mathrm{~m}$ along its sides. Find the angles between the sides.

Fill in the missing parts of this table for triangle $A B C$ .

Solve the oblique triangle $A B C$ if $A=25.1^{\circ}, B=59.0^{\circ}$ , and $b=3.53 \mathrm{~m}$ .

A building is going to be $6.1 \mathrm{~m}$ wide. The roof will be supported by two $4.6-\mathrm{m}$ -rafters. What is the angle at the roof peak? $A building is going to be 6.1 \mathrm{~m} wide. The roof will be supported by two 4.6-\mathrm{m} -rafters. What is the angle at the roof peak?$

Fill in the missing parts of this table for triangle $A B C$ .

Evaluate $\sin^{2} 172^{\circ}-15 \cos^{2} 32^{\circ}$ to four significant digits.

Evaluate, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\theta=\operatorname{arcsec} 12.02$ .

Vector $A$ has magnitude 10.1 while vector $B$ has magnitude 8.63. The angle between the vectors is $2.09 \mathrm{rad}$ . Determine the magnitude $R$ of the resultant and the angle $\theta$ that the resultant makes with the vector $A$ .

Evaluate $\tan^{2} 17^{\circ}+\cos^{2} 17^{\circ}$ to four significant digits.

Solve the oblique triangle $A B C$ if $a=1.5, b=2.2$ , and $c=1$ .1.

In which quadrant will the terminal side of $\theta$ lie if $\theta=-235^{\circ}$ ?

Write the sine, cosine, and tangent of $\theta$ , where $\tan \theta=-4 / 5$ and $\theta$ is not in the fourth quadrant. Leave your answers in fractional or radical form.

Fill in the missing parts of this table for triangle $A B C$ .

Two vectors of magnitude $A=144$ and $B=280$ are separated by an angle $\theta=59.8^{\circ}$ . Find the resultant and the angle the resultant makes with vector $A$ .