Download Lesson 10-5: Right Triangle Trigonometry Mixed

Geometry/Trig
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Date: ________________________
Lesson 10-5: Right Triangle Trigonometry Mixed Practice
Today’s Learning Goal: How can we use trigonometric ratios to solve for a missing part of a right
triangle?
1) Chris is standing on level ground is 2,000 feet away from the foot of a 420-foot-tall building, as shown
in the accompanying diagram. To the nearest degree, what is the value of x?
2) Jake is 70 inches tall casts a shadow of 102 inches. Assuming that he is standing perpendicular to the
ground, what is the angle of elevation from the end of the shadow to the top of Jake’s head, to the nearest
tenth of a degree?
3) Grant, who is eye level is 1.5 m above the ground, stands 30m from a tree. The tree is 10.5m tall. What
is the angle of elevation to a bird at the top of the tree from Grant’s viewpoint to the nearest tenth of a
degree? (Fill in the diagram below to help you! Be careful, we might need to find parts of our diagram!)
Geometry/Trig
4) What is the value of x in the right triangle below? Leave your answer in simplest radical form.
5) Victoria runs diagonally across a rectangular field that has a length of 40 yards and a width of 30
yards, as shown in the diagram below. What is the length of the diagonal that Victoria runs?
6) Raymond placed a ladder against the side of his house as shown in the diagram below. Find the angle
that the ladder makes with the wall to the nearest degree.
Geometry/Trig
7) A tree casts a 25-foot shadow on a sunny day, as shown below. If the angle of elevation from the tip of
the shadow to the top of the tree is 32 degrees, what is the height of the tree to the nearest tenth of a foot?
8) An 8-foot rope is tied from the top of a pole to a stake in the ground. If the rope forms a 57-degree
angle with the ground, what is the height of the pole to the nearest tenth of a foot? Draw a picture first!
9) In right triangle, ABC, AC = 18.3cm and BC = 11.2cm. What is the measure of angle A, to the nearest
degree?
Geometry/Trig
10) A communications company is building a 30-foot antenna to carry cell phone transmissions. Use the
diagram to find the angle that the wire makes with the ground, to the nearest degree.
11) Using triangle ABC, write a ratio to represent the Sin(B):
Hint!
Do you have the
sides you need?
How can you
find them?
Read to challenge yourself?! Ana is standing in a building and looking out of a window at a tree. The tree is 20 feet
away from Ana. Ana’s line of sight to the top of the tree creates a 42o angle of elevation, and her line of sight to the
base of the tree creates a 31o angle of depression.
Hint: Find the two right triangles
and trace over them!
What is the height of the tree?
Round all of your answers to the nearest foot)