Question

Supply the missing information for each of the right triangles described below. In each example, θ = angle, O = opposite side, A = adjacent side, and H = hypotenuse.
sin θ = 0.1736
O = ?
H = 11

Answer 1

Answer:

$\therefore O = 1.9096$

Step-by-step explanation:

Six trigonometric ratio:

• $sin\theta=\frac{opposite}{hypoteuse}$

• $cos\theta=\frac{adjacent}{hypotenuse}$

• $tan \theta=\frac{opposite}{adjacent}$
• $cosec\theta=\frac{hypotenuse}{opposite}$
• $sec\theta=\frac{hypotenuse}{adjacent}$
• $tan \theta=\frac{adjacent}{opposite}$

Given that,

θ = angle,  O= opposite side, A= adjacent side and H = hypotenuse.

H=11, sin θ=0.1736

We know that,

$sin\theta=\frac{opposite}{hypoteuse}$

$\Rightarrow 0.1736=\frac{O}{11}$

$\Rightarrow O = 11 \times 0.1736$

$\Rightarrow O = 1.9096$

$\therefore O = 1.9096$

Answer 2

The missing value is 1.9096

According to SOH CAH TOA identity:

sin θ = opposite/ hypotenuse

Sinθ = O/H

Given the following

• H = 11
• sin θ = 0.1736

Substitute to have:

0.1736 = O/11

O = 11 * 0.1736

O = 1.9096

Hence the missing value is 1.9096

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