Question

How do you do this!!! pls help

Answer 1

`A\approx 110.02 \text{ cm}^2`

`P \approx 53.31 \text{ cm}`

Explanation:

To find the area of a triangle, we need two dimensions: its base and height.

`A_\triangle = (1)/(2)bh`

To find the base of this triangle, we can apply the trigonometric ratio cosine to the right triangle that is half of larger triangle.

`\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}`

↓ plugging in the given values

`\cos(39\°) = ((1)/(2)b)/(15)`

↓ multiplying both sides by 15

`15\cos(39\°) = (1)/(2)b`

↓ multiplying both sides by 2

`30\cos(39\°) = b`

↓ evaluating using a calculator

`b\approx 23.31 \text{ cm}`

To find the height of the triangle, we can apply the Pythagorean Theorem to the right triangle that is half of the larger triangle, now that we know what the base is.

`a^2 + b^2 = c^2`

↓ plugging in the relevant values

`a^2 + \left(\frac{1}2\cdot 23.31\right)^2 = 15^2`

↓ isolating a²

`a^2 = 225 - 135.89`

`a^2 = 89.11`

↓ taking the square root of both sides

`a \approx 9.44`

`h \approx 9.44`

Finally, we can find the area of the triangle.

`A=(1)/(2)bh`

`A=\frac{1}2 \cdot 23.31 \cdot 9.44`

`\boxed{A\approx 110.02 \text{ cm}^2}`

We can find the perimeter by adding the lengths of each side.

`P \approx 15 + 15 + 23.31`

`\boxed{P \approx53.31 \text{ cm} }`