Q: Solve for $x$ if $\sin x = 0.2527$ for $x$ in $[0, 360^\\circ]$. Round to $1$ decimal place.

$14.6^\\circ$ and $165.4^\\circ$

Q: Solve for $x$ if $\sin x = 0.7138$ for $x$ in $[0, 360^\\circ]$. Round to $1$ decimal place.

$45.5^\\circ$ and $134.5^\\circ$

Question 1

A monument has a height of 53.5 feet and the angle of elevation to the top of the monument is $8.13^\circ$. How far away from the monument is the observer standing? (Round to the nearest whole foot.)

Accepted Answer

$377$ feet

Question 2

A radio tower guy wire attaches to the ground at a $71^\circ$ angle and the wire is $1,322$ feet long. How tall is the radio tower to the nearest whole foot?

Accepted Answer

$1,251$ feet

Question 3

A ramp is $4$ feet long and must rise $1$ inch per foot of length. What is the angle of elevation to the nearest tenth of a degree?

Accepted Answer

$1.2^\circ$

Question 4

Solve for $x$ if $\sin x = 0.2527$ for $x$ in $[0, 360^\circ]$. Round to $1$ decimal place.

Accepted Answer

$14.6^\circ$ and $165.4^\circ$

Question 5

Solve for $x$ if $\sin x = 0.7138$ for $x$ in $[0, 360^\circ]$. Round to $1$ decimal place.

Accepted Answer

$45.5^\circ$ and $134.5^\circ$

Question 6

A surveyor stands $200$ feet from the base of a building and measures the angle of elevation to the top as $30^\circ$. What is the height of the building?

Accepted Answer

$115.5$ feet

Question 7

A ladder $20$ feet long leans against a wall, making a $65^\circ$ angle with the ground. How high up the wall does the ladder reach?

Accepted Answer

$18.1$ feet

Question 8

A pilot spots a runway at an angle of depression of $12^\circ$ from a height of $1,500$ feet. How far is the plane from the runway horizontally?

Accepted Answer

$7,180$ feet

Question 9

A tree casts a shadow $25$ feet long when the angle of elevation of the sun is $40^\circ$. What is the height of the tree?

Accepted Answer

$20.1$ feet

Question 10

A ship is $500$ meters from a lighthouse. The angle of elevation to the top of the lighthouse is $5^\circ$. What is the height of the lighthouse?

Accepted Answer

$43.7$ meters

Question 11

A ramp for wheelchair access rises $2$ feet over a horizontal distance of $24$ feet. What is the angle of elevation of the ramp?

Accepted Answer

$4.8^\circ$

Question 12

A firefighter needs to reach a window $30$ feet above the ground. If the ladder must be placed $10$ feet from the building, what angle should the ladder make with the ground?

Accepted Answer

$71.6^\circ$

Question 13

A cable is attached from the top of a $60$ foot pole to the ground $25$ feet away. What is the angle the cable makes with the ground?

Accepted Answer

$67.4^\circ$

Question 14

A person standing $100$ feet from a building sees the top at an angle of elevation of $20^\circ$. How tall is the building?

Accepted Answer

$36.4$ feet

Question 15

A $15$ foot ladder is placed so that it reaches a window $12$ feet above the ground. What is the angle the ladder makes with the ground?

Accepted Answer

$53.1^\circ$

Question 16

A ramp is $10$ feet long and rises $2$ feet. What is the angle of elevation of the ramp?

Accepted Answer

$11.5^\circ$

Question 17

A $25$ foot flagpole casts a shadow $18$ feet long. What is the angle of elevation of the sun?

Accepted Answer

$54.5^\circ$

Question 18

A $40$ foot ladder leans against a building, making a $70^\circ$ angle with the ground. How high up the building does the ladder reach?

Accepted Answer

$37.6$ feet

Question 19

A $50$ foot wire is attached from the top of a pole to the ground $30$ feet away. What is the angle the wire makes with the ground?

Accepted Answer

$53.1^\circ$

Question 20

A $100$ foot building casts a shadow $60$ feet long. What is the angle of elevation of the sun?

Accepted Answer

$59^\circ$

Applications of Trigonometric Functions in Right Triangles

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