The equation $\cos \left(35^{\circ}\right)=\frac{a}{25}$ can be used to find the length of $\overline{B C}$. What is the length of $\overline{B C}$? Round to the nearest tenth.
A. 14.3 in.
B. 20.5 in.
C. 21.3 in.
D. 22.6 in.
Answer (1)
We have the equation cos ( 3 5 ∘ ) = 25 a .
Isolate a by multiplying both sides by 25: a = 25 × cos ( 3 5 ∘ ) .
Calculate the value: a ≈ 20.4788 .
Round to the nearest tenth: 20.5 in.
Explanation
Analyze the problem and given data. We are given the equation cos ( 3 5 ∘ ) = 25 a , which relates the cosine of a 3 5 ∘ angle to the length of side BC , represented by a , and the hypotenuse of length 25. Our goal is to find the length of BC (i.e., the value of a ) rounded to the nearest tenth.
Isolate 'a' in the equation. To find the value of a , we need to isolate it in the equation. We can do this by multiplying both sides of the equation by 25: a = 25 × cos ( 3 5 ∘ )
Calculate the value of a. Now, we calculate the value of 25 × cos ( 3 5 ∘ ) .
The result of this calculation is approximately 20.4788.
Round to the nearest tenth. Finally, we round the calculated value of a to the nearest tenth: a ≈ 20.5
State the final answer. Therefore, the length of BC is approximately 20.5 inches.
Examples
Imagine you are building a ramp that needs to be at a 35-degree angle to the ground. If the length of the ramp (hypotenuse) is 25 inches, you can use the cosine function to determine the horizontal distance (adjacent side) the ramp will cover. This calculation ensures the ramp fits perfectly within the available space, demonstrating a practical application of trigonometry in construction and design.
