In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length

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Question: In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?

Options:

8.66 cm
10 cm
12.25 cm
15 cm

Correct Answer: 8.66 cm

Solution:

Using the Law of Sines: a/sin(A) = b/sin(B). Therefore, b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(45)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * √(3/2) = 8.66 cm.

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length

Practice Questions

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?

8.66 cm
10 cm
12.25 cm
15 cm

Questions & Step-by-Step Solutions

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?

Step 1: Identify the given values in triangle ABC. We have angle A = 45 degrees, side a = 10 cm, and angle B = 60 degrees.
Step 2: Use the Law of Sines formula, which states that a/sin(A) = b/sin(B).
Step 3: Rearrange the formula to find side b: b = a * (sin(B) / sin(A)).
Step 4: Substitute the known values into the formula: b = 10 * (sin(60) / sin(45)).
Step 5: Calculate sin(60) and sin(45). We know that sin(60) = √3/2 and sin(45) = √2/2.
Step 6: Substitute these values into the equation: b = 10 * ((√3/2) / (√2/2)).
Step 7: Simplify the fraction: (√3/2) / (√2/2) = (√3 / √2).
Step 8: Now, substitute back into the equation: b = 10 * (√3 / √2).
Step 9: Simplify further: b = 10 * √(3/2).
Step 10: Calculate the final value: b ≈ 8.66 cm.

Law of Sines – A mathematical formula used to relate the lengths of sides of a triangle to the sines of its angles.
Angle Measures – Understanding the relationship between angles and sides in a triangle, particularly in non-right triangles.
Trigonometric Functions – Utilizing sine values for specific angles to calculate side lengths in triangles.

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length

What’s inside this PDF?

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length

Practice Questions

Questions & Step-by-Step Solutions

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