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Chapter 10: Problem 8

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\mathrm{AC}\) given \(\mathrm{BC}=10 \mathrm{~cm}\) and \(A=40^{\circ}\).

Short Answer

Expert verified
Answer: The length of the side adjacent to the 40° angle is approximately 11.92 cm.

Step by step solution

01

Identify the known values and the required side

In this problem, we know that: - Angle A = 40° - Side BC (opposite to angle A) = 10 cm - Right angle C The required side is AC, which is adjacent to angle A.
02

Set up the Trigonometric Function

Since we are given an angle (40°) and need to find a side adjacent to that angle, we can use the tangent function. The formula for the tangent function in a right triangle is: \(\tan(A) = \frac{\text{opposite side}}{\text{adjacent side}}\) In our problem, we can replace the Angle A and the opposite side length with the given values: \(\tan(40°) = \frac{10}{AC}\)
03

Solve for AC

Now, we just need to solve for AC: \(AC = \frac{10}{\tan(40°)}\) Use a calculator to find the value of \(\tan(40°)\): \(AC = \frac{10}{0.8391}\) Divide the numerator by the denominator: \(AC ≈ 11.92\)
04

Write down the answer

The length of side AC is approximately 11.92 cm.

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Most popular questions from this chapter

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