Right Triangle Trigonometry Worksheet Answer Key Unit 5 Review
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Right Triangle Trigonometry Worksheet Answer Key Unit 5 Review
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. One of the most common types of triangles studied in trigonometry is the right triangle, which has one angle measuring 90 degrees. In Unit 5 of a trigonometry course, students typically learn about right triangle trigonometry, including the trigonometric ratios: sine, cosine, and tangent.
To help students practice and review their understanding of right triangle trigonometry, teachers often provide worksheets with various problems for students to solve. These worksheets typically cover topics such as finding missing sides and angles of right triangles using trigonometric ratios, as well as solving real-world problems involving trigonometry.
Below is a review of a Right Triangle Trigonometry Worksheet Answer Key for Unit 5, which includes solutions to some sample problems that students may encounter on such worksheets.
Problem 1:
In a right triangle, if the length of the hypotenuse is 15 units and the length of one of the legs is 9 units, find the length of the other leg.
Solution:
Let’s denote the length of the other leg as x. According to the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, we have:
x^2 + 9^2 = 15^2
x^2 + 81 = 225
x^2 = 144
x = 12
Therefore, the length of the other leg is 12 units.
Problem 2:
In a right triangle, if the measure of one of the acute angles is 30 degrees and the length of the opposite leg is 8 units, find the length of the hypotenuse.
Solution:
Let’s denote the length of the hypotenuse as h. The trigonometric ratio for sine is defined as the ratio of the length of the opposite leg to the hypotenuse. Therefore, we have:
sin(30 degrees) = 8 / h
1/2 = 8 / h
h = 16
Therefore, the length of the hypotenuse is 16 units.
Problem 3:
A ladder is leaning against a wall such that it forms a right triangle with the ground. If the length of the ladder is 20 feet and the angle between the ladder and the ground is 60 degrees, find the height of the ladder on the wall.
Solution:
Let’s denote the height of the ladder on the wall as h. The trigonometric ratio for sine is defined as the ratio of the length of the opposite leg to the hypotenuse. Therefore, we have:
sin(60 degrees) = h / 20
√3/2 = h / 20
h = 10√3
Therefore, the height of the ladder on the wall is 10√3 feet.
Problem 4:
A ship is traveling in a straight line away from a lighthouse. If the angle of elevation to the top of the lighthouse is 45 degrees and the ship is 500 meters away from the lighthouse, find the height of the lighthouse.
Solution:
Let’s denote the height of the lighthouse as h. The trigonometric ratio for cosine is defined as the ratio of the length of the adjacent leg to the hypotenuse. Therefore, we have:
cos(45 degrees) = h / 500
√2/2 = h / 500
h = 250√2
Therefore, the height of the lighthouse is 250√2 meters.
In Unit 5 of a trigonometry course, students learn about right triangle trigonometry and the trigonometric ratios: sine, cosine, and tangent. By practicing and reviewing problems on worksheets, students can reinforce their understanding of these concepts and improve their problem-solving skills. The Right Triangle Trigonometry Worksheet Answer Key provided above offers solutions to sample problems that students may encounter on such worksheets, helping them to check their work and gain confidence in their ability to apply trigonometric principles to real-world problems.
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