Question

find the area of the triangle given a = 14, c=21, and B=87°. Round your answer to the nearest tenth.​

Answer 1

Answer:   143.8 units²

Step-by-step explanation:

Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:

$Area=\dfrac{1}{2}ac \sin B$

Given: a = 14, c = 21, B = 87°

$Area=\dfrac{1}{2}(14)(21) \sin 87^o\\\\.\qquad =147\sin 87^o\\\\.\qquad =143.8$

Answer 2

Answer:

$\huge \boxed{\mathrm{146.8 \ units^2 }}$

Step-by-step explanation:

We can solve for the area of the triangle when two sides are given and the angle in between the two sides.

$\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }$

$\displaystyle A=\mathrm{\frac{1}{2} \cdot 14 \cdot 21 \cdot sin87 }$

$\displaystyle A=\mathrm{147 \cdot sin87 }$

$\displaystyle A=\mathrm{146.79854160...}$

The area of the triangle is 146.8 units².