Question

The logo shown is symmetrical about one of its diagonals. Enter the angle measures in the green triangle,to the nearest degree. (Hint: First find an angle in a blue triangle.) Then, enter the area of the greentriangle, without first entering the areas of the blue triangles. Round your area to the nearest tenth.

Answer 1

The angle CAE = 37, angle AEC= 72 and angle ACE = 72

The Area is 24.0

The angles of the triangles using the series of steps

1. Since this is a square, all of its corners are 90 degrees

2. We have a measurement for 2 sides of a triangle. Using the equation c^2 = a^2 + b^2. We can calculate the hypotenuse of the triangle

`\begin{gathered} c^2=a^{2^{}}+b^2 \\ c\text{ = }\sqrt[]{4^2+}8^2\text{ = 8.94} \end{gathered}`

3. Using sine law we can get the one side angle of one corner

`\begin{gathered} \frac{8.94}{\sin\text{ 90}}=\text{ }\frac{4}{\sin \text{ }\alpha} \\ \alpha\text{ = }\sin ^(-1)\frac{4\text{ sin 90}}{8.94}\text{ = 26.6} \end{gathered}`

4. We know that one corner of the square is 90 degrees. And since the image is symmetrical to the diagonal, the left blue triangle has also the same angle. We can calculate the angle of the green triangle

`90\text{ - 26.6-26.6 = }36.8`

5. Since that angle inside the triangle has a total measurement of 180 degrees. And the green angle is symmetric.

`(180-36.8)/(2)=71.6`

6. The green triangle has the angles of 36.8, 71.6, and 71.6. They are round up to the nearest degrees 37, 72. and 72.

7. The area is calculated by subtracting the area of blue triangles from the square area.

`8^2\text{ - }(4\ast8)/(2)-(4\ast8)/(2)-(4\ast4)/(2)=\text{ 24.0}`