Question

Given: ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° Find: Area of ∆AFD

Answer 1

To find the area of triangle AFD, use the formula (1/2) * base * height. Substitute the given values and solve using trigonometry. The area of triangle AFD is 49 square units.

Step-by-step explanation:

To find the area of triangle AFD, we can use the formula:

Area = (1/2) * base * height

In triangle AFD, the base is AD and the height is the length of the altitude from point F to line AD. Since angle F is 90°, we can use trigonometry to find this altitude.

sin(30°) = height/AD

By substituting the values we are given, we find that the height is (1/2) * 14 = 7. Therefore, the area of triangle AFD is (1/2) * 14 * 7 = 49 square units.

Answer 2

`(49√(3))/(2)`

Step-by-step explanation:

This is a 30-60-90 triangle. The sides of this triangle can be represented as t (across from the 30° angle since it is the smallest side), 2t (across from the 90° angle since it is the largest side), and t√3 (across from the 60° angle).

Since F is the right angle, this means that AD is across from F and is the hypotenuse. The hypotenuse of a right triangle is the longest side; this means that 2t = 14, so t = 7. This also tells us that t√3 = 7√3.

This means that the height and base of the triangle are 7 and 7√3. Using the formula for the area of a triangle, we have

A = 1/2bh = 1/2(7)(7√3) = 1/2(49√3)

`=(49√(3))/(2)`