Question

What the answer now

Answer 1

Answer:

35.6 yd²

Step-by-step explanation:

Area of ∆UVW can be solved if we know the lengths of 2 sides and their included angle.

We are Given just 1 side, UV (w). Use the law of sines to find UW (v).

Thus:

$\frac{v}{sin(V)} = \frac{w}{sin(W)}$

W = 137°

w = 19 yd

V = 180 - (137 + 22) = 21°  => sum of triangle

v = ??

Plug in the values and solve for v

$\frac{v}{sin(21)} = \frac{19}{sin(137)}$

Multiply both sides by sin(21)

$\frac{v}{sin(21)}*sin(21) = \frac{19}{sin(137)}*sin(21)$

$v = \frac{19*sin(21)}{sin(137)}$

$v = 10 yd$ (approximated)

Find area of ∆UVW:

Area = ½*UV*UW*sin(U)

Area = ½*v*w*sin(U)

= ½*10*19*sin(22)

Area = 35.6 yd² (to nearest tenth)