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Algebra II/Trigonometry Honors
Unit 9 Day 2: Special Right Triangles & Triangle Applications
Special Right Triangle Relationships
Leave each answer in Simplest Radical Form.
1. Ryan quit bowling and took up sailing. His sail for his sailboat is a 45-45-90 Right Triangle. The base of the
sail is 6 ft. long. What would the height of the sail be? What is the length of the hypotenuse?
2. Joe saw a “Yield” sign and “borrowed it.” He wanted to hang it up in his room because it looked cool and it
was in the shape of an Equilateral Triangle. The length of one side is 34 inches. What is the height of the sign?
3. Jeremy is going to show off his skateboarding ability to his Geometry class. He has a skateboard ramp that
must be set up to rise from the ground at 30 ̊. If the height from the ground to the platform is 8 feet, how far is
the ramp to the platform? How long is the ramp up to the top of the platform?
Angles of Sight

Angle of Elevation - __________________________
__________________________________________

Angle of Depression - _________________________
___________________________________________
Determining the Angle in a Right Triangle Application Problem
Find the angle of elevation in the given triangle.
Fun Application Problems!
A parasailer is attached to a boat with a rope 300 feet long. The angle of elevation from the boat to the
parasailer is 48 . Estimate the parasailer’s height above the boat.
A tree casts the shadow shown. What is the height
of the tree?
Find the length of the prop holding up the piano.
The Falls Incline Railway at Niagra Falls has an angle of elevation of 36°. The railway extends a horizontal
distance of about 138 feet. Find the height and length of the railway.
A submersible traveling at a depth of 250 feet dives at an angle of 15° with respect to a line parallel to the
water’s surface. It travels a horizontal distance of 1500 feet during the dive. What is the depth of the
submersible after the dive?
You are climbing Mount Massive in Colorado. You are at an altitude of 11,200 feet. You measure the angle of
elevation to a ridge above you to be 29.4°. The distance (along the face of the mountain) between you and the
ridge is 6315 feet.
 Draw a diagram to represent the situation.

Write and solve an equation to find the altitude of the ridge.
A passenger is an airplane sees two towns directly to the left of the plane.
a) What is the distance d from
the airplane to the first
town?
b) What is the horizontal
distance x from the airplane
to the first town?
c) What is the distance y
between the two towns?
You measure the angle of elevation from the ground to the top of a building as 32°. When you move 50 meters
closer to the building, the angle of elevation is 53°. How high is the building?
HW: Page 560 #3-27 odd, 30, 32