Determine the area of the triangle when tana=1 the image is in the picture above

Question

asked Oct 5, 2022 52.6k views

1 Answer

Kyuuuyki · Answer 1 · 2022-10-10T14:22:39+0000

Answer:

The area will be:

$A=18(1+√(3)) \: u^(2)$ or
$A=49.18 \: u^(2)$ .

Explanation:

Using the definition of tangent, we have:

$tan(\alpha)=\frac{6}{\vec{AB}}$

We know that tan(α) = 1, then we can find AB

$1=\frac{6}{\vec{AB}}$

$\bar{AB}=6\: u$

u means any unit.

Now, we need to find the distance BC. If the angle ∠D is 60°, then ∠C must be 30°. Using the tangent definition in the triangle BCD we have:

$tan(30)=\frac{6}{\bar{BC}}$

$\bar{BC}=(6)/(tan(30))$

$\bar{BC}=(6)/(1/√(3))$

$\bar{BC}=6√(3) \: u$

So, the base of the triangle will be:

$b=\bar{AB}+\bar{BC}=6+6√(3)=6(1+√(3)) \: u$

The area of a triangle is given by the following equation:

A=(b*h)/(2)

A=(6(1+√(3))*6)/(2)

A=18(1+√(3))

Therefore, the area will be
$A=49.18 \: u^(2)$ .

I hope it helps you!