Question

Given the triangle below and the equation: sin A = 3/5.
Determine the value of b.

Answer 1

Using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

Recall:

• The trigonometry ratio is used in solving a right triangle, having, hypotenuse, adjacent, and the opposite side, given a reference angle.

• Trigonometry ratios are: SOH CAH TOA

• Pythagorean Theorem is given as: $c^2 = a^2 + b^2$, where c is the longest side (hypotenuse).

Given the trigonometry ratio of sin A = 3/5

Recall that, sin ∅ = opp/hyp (SOH)

Thus, this means that, in sin A = 3/5,

• A = ∅
• 3 = opposite side, which corresponds to a in the given triangle.
• 5 = hypotenuse, which corresponds to c in the given triangle.
• b is therefore the adjacent side

Thus, find the value of b by applying the Pythagorean theorem.

$b = \sqrt{c^2 - a^2}$ (Pythagorean Theorem)

• Substitute

$b = \sqrt{5^2 - 3^2}\\\\\mathbf{b = 4}$

Therefore, using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

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