Question

In ΔNOP, p = 7.5 inches, ∠O=8° and ∠P=25°. Find the length of n, to the nearest tenth of an inch.

Answer 1

Answer:

Length of n will be 9.7 inches.

Step-by-step explanation:

From ΔNOP in the figure attached,

m∠N + m∠P + m∠O = 180° [Since sum of all interior angles of a triangle = 180°]

m∠N + 25° + 8° = 180°

m∠N = 180° - 33°

m∠N = 147°

Now we will apply Sine rule In the ΔNOP to get the value of side OP.

$\frac{\text{SinP}}{ON}=\frac{\text{SinN}}{OP}$

$\frac{\text{Sin25}}{7.5}=\frac{\text{Sin147}}{n}$

n = $\frac{\text{Sin147}\times 7.5}{\text{Sin25}}$

n = 9.665

n ≈ 9.7 inches

Therefore, length of n will be 9.7 inches.