Question

fall 2025 geometry b wwva
area and perimeter of triangles
which triangles area can be calculated using the trigonometric area formula?

Explanation:

Step1: Recall the trigonometric area formula

The trigonometric area formula for a triangle is $A=\frac{1}{2}ab\sin C$, where $a$ and $b$ are two - side lengths of the triangle and $C$ is the included - angle between them.

Step2: Analyze the first triangle

For the first triangle with vertices $K$, $M$, and $L$, we have side lengths $KM = 15$, $KL=29$, and the included - angle $\angle K = 35^{\circ}$. We can use the formula $A=\frac{1}{2}(15)(29)\sin35^{\circ}$.

Step3: Analyze the second triangle

For the second triangle with vertices $D$, $E$, and $F$, we have side lengths $DE$ and $EF$ (not given explicitly in a way to use the formula directly as we don't know which sides are adjacent to the given angles). But if we assume the sides adjacent to the angles are known, with $\angle D = 34^{\circ}$ and $\angle E=108^{\circ}$, and side lengths related to these angles, we can use the formula. For example, if the sides adjacent to $\angle D$ are $a$ and $b$, then $A=\frac{1}{2}ab\sin D$.

Step4: Analyze the third triangle

For the third triangle with vertices $A$, $B$, and $C$, we have side lengths $AB = 16$, $AC = 28$, but no included - angle between them is given. So we cannot use the trigonometric area formula directly.

We can use the trigonometric area formula for the first and the second triangles.

Answer:

The first and the second triangles.