Right Triangles and Trigonometry: math test, Grade 10 – download the PDF

1 Pythagorean theorem and converse / 4 pts

1. A right triangle has a hypotenuse of \(41\) in and a leg of \(9\) in. Find the other leg.
2. A triangle has sides \(10\) cm, \(24\) cm, and \(26\) cm. Is it a right triangle? Justify.

2 Special right triangles / 3 pts

1. A 45°-45°-90° triangle has a hypotenuse of \(14\) cm. Find its legs (exact value and decimal to the nearest hundredth).
2. A 30°-60°-90° triangle has a long leg of \(9\sqrt{3}\) ft. Find the short leg and the hypotenuse.

3 Geometric mean / 3 pts

In right triangle \(PQR\) (right angle at \(R\)), the altitude from \(R\) divides the hypotenuse \(PQ\) into segments of lengths \(5\) and \(20\). Find the altitude, the hypotenuse, and both legs (exact values, then decimals to the nearest hundredth).

4 Right triangle trigonometry / 4 pts

Calculator allowed. Round to the nearest hundredth for lengths and to the nearest tenth for angles.

1. In a right triangle, an acute angle measures \(62^\circ\) and the leg adjacent to it is \(11\) cm. Find the hypotenuse and the opposite leg.
2. A right triangle has legs \(9\) and \(40\). Find the smaller acute angle.

5 Angle of depression / 3 pts

Calculator allowed. A person on a balcony \(30\) m above the street sees a parked car at an angle of depression of \(25^\circ\).

1. What is the angle of elevation from the car to the person? Explain.
2. How far is the car from the base of the building, to the nearest tenth of a meter?

6 Law of Cosines and Law of Sines / 3 pts

Calculator allowed. In triangle \(ABC\), \(b = 11\), \(c = 16\), and \(A = 52^\circ\).

1. Find \(a\) to the nearest hundredth.
2. Use the Law of Sines to find \(B\) to the nearest tenth of a degree.