Question

What is the area of triangle bcd BC:7 angle b=36

Answer 1

ANSWER

17.8 units²

EXPLANATION

The area of any triangle is half the product between its base and height. In this case, this is,

$A_{BCD}=\frac{1}{2}\cdot BC\cdot CD$

We know that angle B is 36° and its adjacent side, BC, is 7 units long. Since side CD is the opposite side to angle B, we can use the tangent of that angle to find its length,

$\tan B=\frac{opposite}{adjacent}=\frac{CD}{BC}$

Solving for CD,

$CD=BC\tan B=7\tan36\degree\approx5.09$

So, the area is,

$A_{BCD}=\frac{1}{2}\cdot7\cdot5.09\approx17.8\text{ }units^2$

Hence, the area of triangle BCD is 17.8 square units, rounded to the nearest tenth.