Question

Help me please, geometry

Answer 1

Answer:

x = 19.5 (nearest tenth)

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle

• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse (the side opposite the right angle)

Use the cos ratio to find the measure of the altitude (the perpendicular drawn from the vertex of the triangle to the opposite side):

$\implies \cos(47^{\circ})=\dfrac{a}{18}$

$\implies a=18\cos(47^{\circ})$

Now use the sin ratio to the the measure of side x:

$\implies \sin(39^{\circ})=\dfrac{a}{x}$

$\implies x=\dfrac{a}{\sin(39^{\circ})}$

$\implies x=\dfrac{18\cos(47^{\circ})}{\sin(39^{\circ})}$

$\implies x=19.50671018$

Therefore, x = 19.5 (nearest tenth)