QQuestionMathematics
QuestionMathematics
What is the measure of angle A?
# 4
| | | |
| --- | --- | --- |
| 3 cm | 5 cm | |
| | | B |
| | 4 cm | C |
12 months agoReport content
Answer
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Step 1:I'll solve this step by step using the given triangle measurements and LaTeX formatting.
Step 2:: Identify the given information
- $$c = 5 \mathrm{~cm}
- Side lengths:
Step 3:: Recognize this as a right triangle
- The side lengths 3, 4, and 5 form a classic Pythagorean triple - This confirms it's a right triangle with the right angle at vertex C
Step 4:: Use trigonometric functions to find angle A
- $$\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{5}
- In a right triangle, we can use trigonometric functions
Step 5:: Calculate the angle using arccos
- $$A = \arccos\left(\frac{4}{5}\right)
- A = \arccos(0.8)
Step 6:: Convert to degrees
- $$A = \arccos(0.8) \times \frac{180}{\pi}
- A \approx 36.87°
Final Answer
The measure of angle A is approximately 36.87°.
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