Exam 2: Acute Angles and Right Triangles

Solve the problem. -In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at $0.314$ arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about $150,000,000 \mathrm {~km}$ and $\theta = 0.314$ seconds $= \frac { 0.314 } { 60 }$ minutes $= \frac { 0.314 } { 60 \cdot 60 }$ degrees, determine the distance d from Earth to 61 Cygni using Bessel's figures. Express the answer in scientific notation.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 7 }$ and $\mathrm { c } = 6$ .

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -cot ϴ = 1.7009187

Find the reference angle for the given angle. --7.5°

Decide whether the statement is true or false. -sin 86° > sin 24°

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\sin \mathrm { A }$ when $\mathrm { a } = 4$ and $\mathrm { b } = 5$ .

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -cos 31.2°

Solve the problem. -A conservation officer needs to know the width of a river in order to set instruments correctly for a study of pollutants in the river. From point A, the conservation officer walks 100 feet downstream And sights point B on the opposite bank to determine that ϴ = 30° (see figure). How wide is the river (round to the nearest foot)?

Find the exact value of the expression. -sin (-2040°)

Find the exact value of the expression. - $\cot \left( - 1575 ^ { \circ } \right)$

Solve the problem. -A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed, the angle of depression to the car is 45° 56´. When the car Stops, the angle of depression is 22° 34´. The building is 270 feet tall. How far did the car travel from When it was first noticed until it stopped? Round to the nearest foot.

Solve the problem. -The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ϴ where W is the weight of the car and ϴ is the angle of the hill's grade (ϴ > 0 for uphill travel, ϴ < 0 For downhill travel). What is the grade resistance (to the nearest pound)of a 3000-lb car traveling Uphill on a 3° grade (ϴ = 3°)?

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\sec \theta$ is undefined

Find the exact value of the expression. - $\tan 300 ^ { \circ }$

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

Decide whether the statement is true or false. - $\cos 43 ^ { \circ } \leq \cos 5 ^ { \circ }$

Determine whether the statement is true or false. -sin 120° = 2 sin 60° cos 60°

Find the exact value of the expression. -sin 2835°

Solve the problem. -The length of the base of an isosceles triangle is 33.28 meters. Each base angle is 37.57°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -sec ϴ = 2.7259498