Right Triangle Trigonometry: Geometry Math Test – PDF Download

Question 1: Ratios in a right triangle (2 points)

1. Write \(\sin A\), \(\cos A\) and \(\tan A\) as fractions. (1 point)
2. Write \(\sin B\) and \(\cos B\). (1 point)

Question 2: Similar triangles and sine (2 points)

Right triangles ABC and DEF are similar with \(\angle C=\angle F=90^{\circ}\) and \(\angle A\cong\angle D\). In triangle ABC, \(BC=10\) and \(AB=26\). In triangle DEF, \(DE=39\).

1. Find \(EF\). (1 point)
2. Explain why \(\sin A=\sin D\). (1 point)

Question 3: Complementary angles (2 points)

1. Complete: \(\sin 17^{\circ}=\cos\,\underline{\phantom{000}}^{\circ}\). (1 point)
2. Find \(x\) if \(\cos(4x-6)^{\circ}=\sin(x+11)^{\circ}\). (1 point)

Question 4: Special right triangles (2 points)

1. A 45-45-90 triangle has hypotenuse \(10\sqrt{2}\) in. Find the length of each leg. (1 point)
2. A 30-60-90 triangle has a shorter leg of 8 cm. Find the hypotenuse and the longer leg. (1 point)

Question 5: Finding sides (2 points)

Find \(x\) and \(y\) to the nearest tenth. (1 point each)

Question 6: Finding angles (2 points)

1. Find \(m\angle P\) if the side opposite \(P\) is 9 and the hypotenuse is 13. (1 point)
2. Find \(m\angle Q\) if the side opposite \(Q\) is 15 and the side adjacent to \(Q\) is 6. (1 point)

Round each angle to the nearest tenth of a degree.

Question 7: Solve a right triangle (3 points)

Solve the triangle: find \(AB\), \(m\angle A\) and \(m\angle B\). Round to the nearest tenth. (1 point each)

Question 8: Angle of depression (3 points)

How far is the sailboat from the base of the cliff? Round to the nearest tenth of a foot. (3 points)

Question 9: Zip line (2 points)

A zip line cable runs from a platform 32 ft above level ground to the ground, and the cable makes a \(25^{\circ}\) angle with the ground. Find the length of the cable and the horizontal distance it covers. Round to the nearest tenth of a foot. (1 point each)

⬇ Download the Geometry Right Triangle Trigonometry test (PDF, 90 KB)

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