Exam 6: Trigonometric Functions: Unit Circle Approach

To find the distance across a river a surveyor chooses points $A$ and $B$ , $50$ m apart and a reference point $C$ on the opposite side of theriver. Approximate the distance, $b$ , between $A$ and $C$ given that $\angle \mathrm { A } =54 ^ { \circ }$ and $\angle B = 77 ^ { \circ }$ .

Find the radian measure that corresponds to each degree measure. $315 ^ { \circ }$ , $- 225 ^ { \circ }$

Solve for $x$ correct to one decimal place.

Land in downtown Stevensville is valued at $\$ 20$ a square foot. What is the value of a triangular lot with sides of lengths 112ft, 148ft, and 190 ft?

From the top of a $250$ ft lighthouse, the angle of depression to a ship in the ocean is $18 ^ { \circ }$ ) How far is the ship from the base of the lighthouse?

Solve for $x$ correct to one decimal place.

Find the area of a triangle with sides of length 12 and 22 and included angle $10 ^ { \circ }$

Find the radian measures that correspond to the degree measures $- 1080 ^ { \circ }$ and $15 ^ { \circ }$ .

Find the exact value of the expression. $\left( \sin 60 ^ { \circ } \right) ^ { 2 } - \left( \cos 60 ^ { \circ } \right) ^ { 2 }$

To find the distance across a river a surveyor chooses points $A$ and $B$ , $50$ M apart and a reference point $C$ On the opposite side of theriver. Approximate the distance, $b$ , between $A$ And $C$ Given that $\angle\mathrm { A } = 54 ^ { \circ }$ And $\angle B = 77 ^ { \circ }$

How many revolutions will a bicycle wheel of diameter $26$ inches make as the bicycle travels a distance of $4$ Miles?

Find the acute angle that is formed by the line $y - \sqrt { 3 } x + 1 = 0$ and the x-axis

Find the area of a sector with central angle $120 ^ { \circ }$ in a circle with radius $12$ M

Find the radian measure that corresponds to each degree measure. $300 ^ { \circ }$ , $- 300 ^ { \circ }$

Find the measure of the central angle $\theta$ in a circle of radius 6 ft if the angle is subtended by an arc of length 7 ft.

Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$

Solve for $x$ correct to one decimal place.

Find the area of a triangle with sides of length 12 and 22 and included angle $10 ^ { \circ }$ . Round the answer to one decimal place.

A plane leaves the airport at 4:00 p.m. and heads in the direction N $10 ^ { \circ }$ E at a constant speed of $250$ mi/h. Forty-five minutes later, a jet leaves the same airport and flies N $60 ^ { \circ }$ W at a constant speed of $450$ mi/h. Find the distance between the plane and the jet at 5:30 p.m

Solve for $x$ correct to one decimal place.