Q: A right triangle has one angle measuring $$34^\\circ 30'$$ and hypotenuse $$c = 12.7$$ inches. What is the length of side $$b$$ adjacent to the given angle?

$$b = 12.7 \\cos(34.5^\\circ)$$

Q: Given a right triangle with legs $$a = 29.43 cm $$and hypotenuse $$c = 53.58 cm$$, what is the measure of angle $$A$$ opposite side $$a$$?

$$A = \\arcsin(29.43 / 53.58)$$

Q: A building is $$34.09$$ meters tall and casts a shadow $$37.62$$ meters long. What is the angle of elevation of the sun?

$$\\theta = \\arctan(34.09 / 37.62)$$

Q: The parallax angle to Alpha Centauri is $$0.000212^\\circ$$ and the Earth-Sun distance is $$93,000,000$$ miles. What is the distance $$d to $$Alpha Centauri in miles?

$$d = 93,000,000 / \\tan(0.000212^\\circ)$$

Q: Francisco measures the angle of elevation to the top of a tree as $$36.7^\\circ$$ from point A, then $$22.2^\\circ$$ from a point $$50 ft $$further away. What equation relates the height $$h of $$the tree to the unknown distance $$x$$ from the first point?

$$h = x \\tan(36.7^\\circ)$$ and $$h = (x + 50) \\tan(22.2^\\circ)$$

Q: Which trigonometric function would you use to find the height of a building if you know the length of its shadow and the angle of elevation of the sun?

$$\\tan(\\theta) = \\frac{\\text{height}}{\\text{shadow}}$$

Q: A star has a parallax angle $$\\theta$$ and the Earth-Sun distance is $$d_0. $$Which formula gives the distance $$d to $$the star?

$$d = \\frac{d_0$}{\\tan(\\theta)}$$

Question 1

A right triangle has one angle measuring $$34^\circ 30'$$ and hypotenuse $$c = 12.7$$ inches. What is the length of side $$b$$ adjacent to the given angle?

Accepted Answer

$$b = 12.7 \cos(34.5^\circ)$$

Question 2

Given a right triangle with legs $$a = 29.43 cm $$and hypotenuse $$c = 53.58 cm$$, what is the measure of angle $$A$$ opposite side $$a$$?

Accepted Answer

$$A = \arcsin(29.43 / 53.58)$$

Question 3

A building is $$34.09$$ meters tall and casts a shadow $$37.62$$ meters long. What is the angle of elevation of the sun?

Accepted Answer

$$\theta = \arctan(34.09 / 37.62)$$

Question 4

Which of the following best describes the angle of depression?

Accepted Answer

The acute angle formed by a line of sight downward from a horizontal line

Question 5

A radar station A is west of station B by $$3.70 km. $$Station A detects a plane at C on a bearing of $$61.0^\circ$$, and station B detects the same plane at a bearing of $$331.0^\circ. $$What is the measure of angle $$CAB at $$station A?

Accepted Answer

$$CAB = 61.0^\circ$$

Question 6

A plane travels from A to B at $$250$$ mph for $$2.4$$ hours. What is the distance from A to B?

Accepted Answer

$$600$$ miles

Question 7

If a runway is labeled $$12L$$, what is the corresponding right runway number?

Accepted Answer

$$30R$$

Question 8

The parallax angle to Alpha Centauri is $$0.000212^\circ$$ and the Earth-Sun distance is $$93,000,000$$ miles. What is the distance $$d to $$Alpha Centauri in miles?

Accepted Answer

$$d = 93,000,000 / \tan(0.000212^\circ)$$

Question 9

Francisco measures the angle of elevation to the top of a tree as $$36.7^\circ$$ from point A, then $$22.2^\circ$$ from a point $$50 ft $$further away. What equation relates the height $$h of $$the tree to the unknown distance $$x$$ from the first point?

Accepted Answer

$$h = x \tan(36.7^\circ)$$ and $$h = (x + 50) \tan(22.2^\circ)$$

Question 10

Which of the following is the correct formula for the length of the side $$b in a $$right triangle with sides $$a$$, $$b$$, and hypotenuse $$c$$?

Accepted Answer

$$b = \sqrt{c^2$ - a^2$}$$

Question 11

A bearing is given as S $$52^\circ E. $$Which direction does this indicate?

Accepted Answer

52 degrees east of due south

Question 12

If the angle of elevation from a point on the ground to the top of a building increases, what happens to the length of the building's shadow (assuming the building's height is constant)?

Accepted Answer

The shadow becomes shorter

Question 13

A pilot turns right onto runway $$30R. $$What is the bearing of the plane at takeoff?

Accepted Answer

$$300^\circ$$

Question 14

Which trigonometric function would you use to find the height of a building if you know the length of its shadow and the angle of elevation of the sun?

Accepted Answer

$$\tan(\theta) = \frac{\text{height}}{\text{shadow}}$$

Question 15

A star has a parallax angle $$\theta$$ and the Earth-Sun distance is $$d_0. $$Which formula gives the distance $$d to $$the star?

Accepted Answer

$$d = \frac{d_0$}{\tan(\theta)}$$

Question 16

Which of the following steps is NOT part of solving an applied trigonometry problem?

Accepted Answer

Guessing the answer based on intuition

Applications of Right Triangles and Trigonometry: The Unit Circle and Beyond

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