Question

Find the area diagram below: Round to the nearest tenth.

30°
18m
1403
70.1
187
12

Answer 1

70.1

Explanation:

This is a 30-60-90 right triangle.

The ratio of side lengths is as follows:

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

The short leg is 1/2 the hypotenuse.

The long leg is sqrt(3) times the short leg.

A = bh/2

A = (18/2)(18/2 * sqrt(3))/2

A = 70.1

Answer 2

The answer is option 2.

Explanation:

First, you have to find the height of the triangle using Cosine Rule, cosθ = adjacent/hypotenuse :

`cos(θ) = (adj.)/(hypo.)`

`θ = 30,adj. = h,hypo = 18`

`\cos(30) = (h)/(18)`

`18 \cos(30) = h`

`h = 9 √(3) \: m`

Next, you have to find the area of triangle using Sin Rule, Area = 1/2×a×b×sinC where a, b represent the side length of the angle and C is the angle :

`area = (1)/(2) * a * b * sin(C)`

`let \: a = 9 √(3) ,b = 18,C = 30`

`area = (1)/(2) * 9 √(3) * 18 * \sin(30)`

`area = 70.1 \: {m}^(2) \: (near.tenth)`