Q: A right triangle has an angle $A = 34^ ext{\circ} 30'$ and hypotenuse $c = 12.7$ inches. What is the length of side $a$ opposite angle $A$? (Round to two decimal places.)

$a = 12.7 \sin 34^\text{\circ} 30' \approx 7.19$ inches

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

$A = \arcsin \left( \frac{29.43}{53.58} \right) \approx 33.32^\text{\circ}$

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

$\tan B = \frac{34.09}{37.62}$, $B = \arctan \left( \frac{34.09}{37.62} \right) \approx 42.18^\text{\circ}$

Q: A radar station A is west of station B by 3.70 km. A plane is detected at C, with bearings of $61.0^\text{\circ}$ from A and $331.0^\text{\circ}$ from B. What is the distance from A to C?

$b = 3.70 \cos 29.0^\text{\circ} \approx 3.24$ km

Q: Given the bearings S $52^\text{\circ}$ E from A to C, N $84^\text{\circ}$ E from A to B, and S $38^\text{\circ}$ W from B to C, and the distance from A to B is 600 miles, what is the distance from A to C if $\angle BAC = 46^\text{\circ}$?

$b = 600 \sin 46^\text{\circ} \approx 430$ miles

Q: If a runway is labeled 12L, what is the number of the corresponding right runway (R) and what is the bearing of the right runway?

30R, bearing $300^\text{\circ}$

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

$d = \frac{93,000,000}{\sin 0.000212^\text{\circ}} \approx 2.51 \times 10^{13}$ miles

Q: If the distance to Alpha Centauri is $2.51 \times 10^{13}$ miles and a light-year is $5.9 \times 10^{12}$ miles, what is the distance to Alpha Centauri in light-years?

$\frac{2.51 \times 10^{13}}{5.9 \times 10^{12}} \approx 4.3$ light-years

Q: Francisco stands at a point where the angle of elevation to the top of a tree is $36.7^\text{\circ}$. He moves back 50 feet and the angle of elevation becomes $22.2^\text{\circ}$. What is the height of the tree?

$h = \frac{50 \tan 22.2^\text{\circ}}{\tan 36.7^\text{\circ} - \tan 22.2^\text{\circ}} \tan 36.7^\text{\circ} \approx 45$ feet

Question 1

A right triangle has an angle $A = 34^	ext{\circ} 30'$ and hypotenuse $c = 12.7$ inches. What is the length of side $a$ opposite angle $A$? (Round to two decimal places.)

Accepted Answer

$a = 12.7 \sin 34^	ext{\circ} 30' \approx 7.19$ inches

Question 2

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

Accepted Answer

$A = \arcsin \left( \frac{29.43}{53.58} ight) \approx 33.32^	ext{\circ}$

Question 3

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

Accepted Answer

$	an B = \frac{34.09}{37.62}$, $B = \arctan \left( \frac{34.09}{37.62} ight) \approx 42.18^	ext{\circ}$

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 to an object below.

Question 5

A radar station A is west of station B by 3.70 km. A plane is detected at C, with bearings of $61.0^	ext{\circ}$ from A and $331.0^	ext{\circ}$ from B. What is the distance from A to C?

Accepted Answer

$b = 3.70 \cos 29.0^	ext{\circ} \approx 3.24$ km

Question 6

A plane flies from A to B on a bearing of N $84^	ext{\circ}$ E for 2.4 hours at 250 mph. What is the distance from A to B?

Accepted Answer

$250 	imes 2.4 = 600$ miles

Question 7

Given the bearings S $52^	ext{\circ}$ E from A to C, N $84^	ext{\circ}$ E from A to B, and S $38^	ext{\circ}$ W from B to C, and the distance from A to B is 600 miles, what is the distance from A to C if $\angle BAC = 46^	ext{\circ}$?

Accepted Answer

$b = 600 \sin 46^	ext{\circ} \approx 430$ miles

Question 8

If a runway is labeled 12L, what is the number of the corresponding right runway (R) and what is the bearing of the right runway?

Accepted Answer

30R, bearing $300^	ext{\circ}$

Question 9

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

Accepted Answer

$d = \frac{93,000,000}{\sin 0.000212^	ext{\circ}} \approx 2.51 	imes 10^{13}$ miles

Question 10

If the distance to Alpha Centauri is $2.51 	imes 10^{13}$ miles and a light-year is $5.9 	imes 10^{12}$ miles, what is the distance to Alpha Centauri in light-years?

Accepted Answer

$\frac{2.51 	imes 10^{13}}{5.9 	imes 10^{12}} \approx 4.3$ light-years

Question 11

Francisco stands at a point where the angle of elevation to the top of a tree is $36.7^	ext{\circ}$. He moves back 50 feet and the angle of elevation becomes $22.2^	ext{\circ}$. What is the height of the tree?

Accepted Answer

$h = \frac{50 	an 22.2^	ext{\circ}}{	an 36.7^	ext{\circ} - 	an 22.2^	ext{\circ}} 	an 36.7^	ext{\circ} \approx 45$ feet

Question 12

Which of the following is the correct process for solving an applied trigonometry problem involving right triangles?

Accepted Answer

Draw a sketch, write an equation relating the given quantities, solve the equation, and check your answer.

Question 13

If a right triangle has legs $a = 29.43$ cm and $b = 44.77$ cm, what is the length of the hypotenuse $c$?

Accepted Answer

$c = \sqrt{29.43^2 + 44.77^2} \approx 53.58$ cm

Question 14

Which of the following best describes the first method for expressing bearing?

Accepted Answer

A single angle measured clockwise from north.

Question 15

A surveyor needs to find the height of a building. From a point 80 meters from the base, the angle of elevation to the top is $28^	ext{\circ}$. What is the height of the building?

Accepted Answer

$h = 80 	an 28^	ext{\circ} \approx 42.6$ meters

Applications of Right Triangles in Trigonometry

Study Guide - Practice Questions

Study Guide - Flashcards