Solve the right triangle ABC where $ C = 90^\circ $. Given $ A = 35.6^\circ $ and $ b = 35.9 \, \text{cm} $, find the length of side $ a $ in centimeters. Round your answer to the nearest tenth.

Options:
A) 36.2 cm
B) 37.5 cm
C) 34.8 cm
D) 35.4 cm

Question

10-08-2024
Mathematics

High School

Thank you for visiting Solve the right triangle ABC where C 90 circ Given A 35 6 circ and b 35 9 text cm find the length of side. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Solve the right triangle ABC where $ C = 90^\circ $. Given $ A = 35.6^\circ $ and $ b = 35.9 \, \text{cm} $, find the length of side $ a $ in centimeters. Round your answer to the nearest tenth.

Options:
A) 36.2 cm
B) 37.5 cm
C) 34.8 cm
D) 35.4 cm

Answer :

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Final answer:

To find the value of side a in triangle ABC, we first find angle B using the sum of angles in a triangle, then apply the tangent ratio for angle A to solve for a. The calculation gives an approximate value of 25.8 cm for side a, which does not match any of the provided options.

Explanation:

To solve for the value of a in the right triangle ABC with C = 90 degrees, A = 35.6 degrees, and b = 35.9 cm, we first determine the angle B. Since the sum of angles in any triangle is 180 degrees, we can find angle B by subtracting the known angles from 180 degrees:

B = 180 degrees - A - C

B = 180 degrees - 35.6 degrees - 90 degrees

B = 54.4 degrees

Now we'll use the tangent of angle A to find the length of side a, knowing the length of side b:

tan(A) = opposite/adjacent

tan(35.6 degrees) = a / 35.9 cm

Multiplying both sides by 35.9 cm to isolate a:

a = 35.9 cm * tan(35.6 degrees)

Calculating the value of tan(35.6 degrees) and multiplying by 35.9 cm yields the value of a:

a \u2248 35.9 cm * 0.7162

a \u2248 25.7 cm

Rounded to the nearest tenth, the value of a is 25.8 cm, which is not listed in the options provided.

Solve the right triangle ABC where \( C = 90^\circ \). Given \( A = 35.6^\circ \) and \( b = 35.9 \, \text{cm} \), find the length of side \( a \) in centimeters. Round your answer to the nearest tenth.Options:A) 36.2 cm B) 37.5 cm C) 34.8 cm D) 35.4 cm

Answer :

Final answer:

Explanation:

Other Questions

Solve the right triangle ABC where \( C = 90^\circ \). Given \( A = 35.6^\circ \) and \( b = 35.9 \, \text{cm} \), find the length of side \( a \) in centimeters. Round your answer to the nearest tenth.

Options:
A) 36.2 cm
B) 37.5 cm
C) 34.8 cm
D) 35.4 cm