Math Problem Statement
Find m>B to the nearest tenth
Solution
To find the measure of angle (denoted as ) in the given right triangle , we can use trigonometric functions. Here’s how:
Step 1: Identify the sides
In the right triangle :
- (Opposite side relative to )
- (Hypotenuse)
Step 2: Use the sine function
The sine of angle is given by:
Step 3: Calculate
Step 4: Find using the inverse sine function
Step 5: Calculate the angle
Using a calculator or trigonometric tables:
Thus, the measure of angle is approximately 56.4° to the nearest tenth.
Would you like any further details or have any questions?
Here are 5 related questions:
- How can we use the cosine function to find in the same triangle?
- What is the measure of angle in ?
- Can we use the tangent function to find ? If so, how?
- How do you determine which trigonometric function to use based on given sides?
- 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