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Find the missing sides and angle in the right triangle ABC, given that \( C = 90^\circ \), \( A = 35.5^\circ \), and \( b = 37.6 \, \text{ft} \).

Answer :

Final answer:

To find the missing sides and angle in the right triangle ABC, use trigonometric ratios. Given angle A and side b, use the Pythagorean theorem to find side c. Then, use cosine and sine to find sides a and c, and angle C.

Explanation:

To find the missing sides and angle in the right triangle ABC, we can use trigonometric ratios. Given that angle A is 35.5° and side b is 37.6ft, we can find side c using the Pythagorean theorem. Using sine and cosine, we can find the other two sides, a and c, and angle C.

Using the Pythagorean theorem: c² = a² + b²

Using cosine: a = b * cos(A)

Using sine: c = b * sin(A)

Therefore, side a is approximately 30.98ft, side c is approximately 21.32ft, and angle C is approximately 53.5°.

Learn more about trigonometry here:

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