Word Problems
A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11degrees∘. 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.
(Delta Math)
The ship is 581.3 feet from the lighthouse.
Is it possible to form a triangle with the side lengths 8, 15, and 17?
Yes.
In triangle DEF, m<F = 45°, m<E = 90°, and f = 8. Find the length of DF.
8√ 2
In triangle LMN, l = 9.8, m = 18, and m<M = 90°. Find the measure of angle L. Round to nearest tenth.
33°
In triangle ABC, m∠A = 81.5°, m∠B = 41°, and c = 17. Find b.
13.2
The angle of elevation to a nearby tree from a point on the ground is measured to be 54degrees∘. How tall is the tree if the point on the ground is 89 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.
(Delta Math)
The tree is 122.5 feet tall.
Is it possible to form a triangle with the side lengths 2, 8, and 11.
No.
In triangle NEW, m<N = 45°, m<E = 90°, and e = 15√ 2. Find the length of NE.
15
In triangle EFG, e = 48, f = 60, and m<F = 90°. Find the measure of angle E. Round to nearest tenth.
53.1°
In triangle ABC, m∠A = 30°, m∠B = 65°, and a = 8.7. Find b.
15.8
From the observation deck of a skyscraper, Meena measures a 48degrees∘ angle of depression to a ship in the harbor below. If the observation deck is 1068 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
(Delta Math)
The base of the skyscraper is 961.6 feet from the ship.
Classify the triangle with the side lengths 7, 14, and 16. (Acute, Obtuse, or Right).
Obtuse.
In triangle ABC, m<A = 45°, m<B = 90°, and b = 14. Find the length of BC.
7√ 2
In triangle HIJ, i = 18, j = 9, and m<I = 90°. Find the measure of angle J. Round to nearest tenth.
30°
In triangle ABC, m∠A = 65°, a = 9.5, and b = 6. Find m∠B (in degrees).
34.9
From a hot-air balloon, Adriel measures a 22 degrees∘ angle of depression to a landmark that’s 743 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
(Delta Math)
The balloon is 300.19 feet above the ground.
Classify the triangle with the side lengths 15, 20, and 24. (Obtuse, Acute, or Right).
Acute.
In triangle IJK, m<L = 45°, m<K = 90°, and k = 22. Find the length of JK.
11√ 2
In triangle HIJ, h = 8.1, j = 4.4, and m<I = 90°. Find the measure of angle H. Round to nearest tenth.
61.5°
Two freight trains leave at the same time from the same station. The angle between the two tracks on which they leave is 110°. One travels at an average speed of 30 mph and the other at an average speed of 40 mph. How far apart are they (in miles) after 30 minutes?
28.8
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, 8degrees∘. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
(Delta Math)
The ship is 1053.07 feet from the lighthouse.
Is the following set of side lengths Pythagorean triple?
15, 25, and 30.
No.
In triangle ABC, m<A = 30°, m<B = 60°, and b = 5√ 3. Find the length of AB.
10
In triangle GHI, h = 9.5, i = 4.1, and m<H = 90°. Find the measure of angle G. Round to nearest tenth.
64.4°
In triangle ABC, m∠A = 64°, a = 6, and b = 7. Find m∠B.
No such triangles exist.