Math Problem Statement

Find m>B to the nearest tenth

Find m∠B to the nearest tenth

Solution

To find the measure of angle B\angle B (denoted as mBm\angle B) in the given right triangle ABC\triangle ABC, we can use trigonometric functions. Here’s how:

Step 1: Identify the sides

In the right triangle ABCABC:

  • AB=25AB = 25 (Opposite side relative to B\angle B)
  • BC=30BC = 30 (Hypotenuse)

Step 2: Use the sine function

The sine of angle BB is given by: sinB=OppositeHypotenuse=ABBC=2530\sin B = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{AB}{BC} = \frac{25}{30}

Step 3: Calculate sinB\sin B

sinB=2530=560.8333\sin B = \frac{25}{30} = \frac{5}{6} \approx 0.8333

Step 4: Find B\angle B using the inverse sine function

B=sin1(0.8333)B = \sin^{-1}(0.8333)

Step 5: Calculate the angle

Using a calculator or trigonometric tables: Bsin1(0.8333)56.4B \approx \sin^{-1}(0.8333) \approx 56.4^\circ

Thus, the measure of angle BB is approximately 56.4° to the nearest tenth.

Would you like any further details or have any questions?


Here are 5 related questions:

  1. How can we use the cosine function to find mAm\angle A in the same triangle?
  2. What is the measure of angle CC in ABC\triangle ABC?
  3. Can we use the tangent function to find mBm\angle B? If so, how?
  4. How do you determine which trigonometric function to use based on given sides?
  5. How does the Pythagorean theorem confirm the accuracy of the given side lengths?

Tip: For solving right triangles, always check if you can apply the Pythagorean theorem before using trigonometric functions. This can help verify that the triangle sides are correct.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle

Formulas

sin(θ) = Opposite / Hypotenuse
Inverse sine function: θ = sin^(-1)(value)

Theorems

Basic Trigonometric Ratios
Inverse Trigonometric Functions

Suitable Grade Level

Grades 9-10