Question: Unit E: Trigonometry
Chapter 10 Practice
c.
15 ft
25 ft
We know
3
3
3
Triangle shape in the center-right: a right triangle with left vertical side labeled 15 ft, slanted top side labeled 25 ft, and an unlabeled bottom side; position_hint = center-right.
1. **Problem Statement:**
We have a right triangle with one leg measuring $15$ ft and the hypotenuse measuring $25$ ft. We need to find the length of the other leg.
2. **Formula Used:**
In a right triangle, the Pythagorean theorem applies:
$$a^2 + b^2 = c^2$$
where $c$ is the hypotenuse, and $a$, $b$ are the legs.
3. **Identify Known Values:**
Let the unknown leg be $b$.
Given:
$$a = 15$$
$$c = 25$$
4. **Apply the Pythagorean theorem:**
$$15^2 + b^2 = 25^2$$
$$225 + b^2 = 625$$
5. **Isolate $b^2$:**
$$b^2 = 625 - 225$$
$$b^2 = 400$$
6. **Find $b$ by taking the square root:**
$$b = \sqrt{400}$$
$$b = 20$$
7. **Answer:**
The length of the other leg is $20$ ft.