Trig Ratios #2

Last updated 11 months ago

17 questions

Find the missing side lengths.  Leave your answers as radicals in simplest form.

x=_______ 
y=_______ 

Find the missing side lengths.  Leave your answers as radicals in simplest form.


x=_______ 
y=_______ 

Find the missing side lengths.  Leave your answers as radicals in simplest form.

x=_______ 
y=_______ 

Find the area of the triangle. Use A=\frac{1}{2}bh.
Leave your answer in radical form.
A=_______ u^2

Find the missing side lengths.  Leave your answers as radicals in simplest form.


x=_______ 
y=_______ 

Find the area of the triangle. Use A=\frac{1}{2}bh.
Leave your answer in radical form.

A=_______ u^2

Use your calculator to find each of the following. Round your answers to the nearest thousandth. (3 places after the decimal)
cos( 25\degree)=_______ 
sin (65\degree)=_______ 
sin (41\degree)=_______ 
cos(49\degree)=_______ 
sin(11\degree)=cos(_______ )
cos(x\degree)=sin(_______ )

SIN=\frac{Opposite}{Hypotenuse}

Find the sine ratio for each angle indicated:
Sin( X)=_______
Sin (Z)=_______

Find the missing side.  Round to the nearest tenth.

x=_______ units

A guy wire is a wire used to anchor a tower or other structure in place. In the picture below, a guy wire helps to anchor a cell phone tower in place. It is connected to the tower 150 feet above the ground. Round your answers to the nearest tenth of a foot.

How long is the guy wire if the angle between the ground and the wire is 50\degree?_______ feet

How far from the tower is the guy wire anchored to the ground? _______ feet

Find the cosine ratio for each angle indicated:
Be sure to reduce the fraction to lowest terms.

Cos(X)=_______ 

Cos(Z)=_______ 

Find the missing side.  Round to the nearest tenth.

x=_______ units

The line of sight distance is the distance from one position to another. 

In the picture, what is the line of sight distance from a person standing on the ground at point A to a person on the observation deck at the top of the building if the angle of the person looking up is 66\degree?
(Round your answer to the nearest foot) _______ feet

How tall is the building? _______ feet
(For purposes of this problem, ignore the height of the person when finding the height of the building.)

Find the cosine ratio for each angle indicated:
Be sure to reduce the fraction to lowest terms.

Tan(X)=_______ 

Tan(Z)=_______ 

Find the missing side.  Round to the nearest tenth.

x=_______ units

A 25 foot pole has a guy wire attached at the top of the pole and makes a 52\degree angle  where it is attached to the ground. Round your answers to the nearest tenth of a foot.

How far from the pole is the wire attached to the ground? _______ feet

Ignoring the extra length needed to attach the guy wire, how long must the guy wire be? _______ 

Frank is out on a windy day flying his kite. He has 100 feet of line that he has let out completely. He measures the angle the line makes with the ground and finds it is 25\degree.
He measured the angle from 3 feet off the ground. He wants to know how high his kite is from the ground.

The kite is _______ feet in the air.

If Frank has a friend standing directly under the kite, how far is Frank standing from his friend? _______ feet.

The lighthouse is _______ m tall.
What is the line of sight distance to the top of the lighthouse?_______ m

(Note: The 29\degree angle shown is also the angle the boat makes with the water since they are alternate interior angles.) 

How far is the boat from the lighthouse? _______ meters