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HG U5D8 Right Tri. Word Problems Oct23

Last updated 7 months ago
23 questions
1. Read the problem. What is given? What are you asked to find?
2. Draw a diagram.
3. Set up an equation.
4. Solve it.
5. Make sure your answer is the answer to the question.
1
Express the trig ratios as fractions.

cos X = _______

sin Y = _______

tan X = _______
1
Express the trig ratios as fractions.

sin R = _______

cos Q = _______

tan R = _______
1
If you place a 24-foot ladder against the top of a 20-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
The distance from the bottom of the building to the bottom of the ladder is _______ feet.
Example Diagrams:



To solve it:
1. Read the problem. What is given? What are you asked to find?
2. Draw a diagram.
3. Set up an equation.
4. Solve it.
5. Make sure your answer is the answer to the question.
1

From her eye, which stands 1.66 meters above the ground, Deondra measures the angle of elevation to the top of a prominent skyscraper to be 70o. If she is standing at a horizontal distance of 276 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.

To solve it:
1. Read the problem. What is given? What are you asked to find?
2. Draw a diagram.
3. Set up an equation.
4. Solve it.
5. Make sure your answer is the answer to the question.

1

From the observation deck of a tower, Meena measures a 48o angle of depression to a ship in the harbor below. If the observation desk is 1068 feet high, what is the horizontal distance from the base of the tower out to the ship? Round you answer to the nearest tenth of a foot if necessary.

1

Makayla leans a 26-foot ladder against a wall so that if forms an angle of 69o with the ground. What is the horizontal distance between the base of the ladder and the bottom of the wall? Round your answer to the nearest tenth of a foot if necessary.

1

A boat is heading towards a lighthouse, whose beacon-light is 148 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 8o. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.

1

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 27 feet up. The ladder makes an angle of 62o with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

1

Scale Factor
Anna is creating a mural from a drawing. If the drawing is 10 inches wide and the mural will be 8 feet wide, what is the scale factor of the dilation relating the drawing to the mural?

1

A square with sides of 15 feet is dilated with a scale factor of 0.2, what is the area of the dilated square?

1

Are the two triangles similar? Explain how you know.

1

The sides of a triangle measure 13 inches, 16 inches and 20 inches.
Could this be a right triangle? Explain how you know and show your work.

1
A certain television is advertised as a 95-inch TV (the diagonal length). If the width of the TV is 77 inches, how tall is the TV? Round to the nearest tenth of an inch.
height of TV = _______ inches
1
Are the two triangles similar? If they are, complete the similarity statement.
∆KIJ ~ ∆_______
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______o
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______o
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______
1
Solve for x. Round to the nearest tenth, if necessary.
x = _______o
1
In ΔEFG, the measure of ∠G=90°, GF = 40, FE = 41, and EG = 9.
What is the tangent of ∠F?
tan F = _______
What is the measure of ∠F? Round to the nearest tenth.
m∠F = _______o
1

Aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. She measures the angle of elevation from her hand to the kite to be 25o. If the string from the kite to her hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.