Question

2) The measure of each base angle of an isosceles triangle is 30 degrees and each of the two congruent sides has a length of 14 inches. How long is the base? What is the area of the triangle?

Answer 1

Answer:

true or false = Puranas advocated that one could receive the grace of god regardless of caste status.

Answer 2

The length of the base is 14√3 inches

The area of the triangle is 49√3 inches

Given,

The measure of each base angle of an isosceles triangle = 30 degrees

Each of the two congruent sides has a length = 14 inches

To find,

The length of the base and the area of the triangle

Solution,

Draw an isosceles triangle with the data given, (see the attached picture below)

Let us assume the length of the base be a

To find the length of the base,

cos Θ = Base / Hypotenuse

cos 30° = (a /2 ) / (14/7)

√3/2 = a/28

a = 14√3 inches

Now, to find the area of the triangle, the formula is Area = 1/2 * base * height

Let us assume the height of the triangle be x,

To find the height,

sin Θ = opposite side / hypotenuse

sin 30° = x / 14

1/2 = x/14

x = 7  inches

Area = 1/2 * 14√3 * 7

Area = 49√3

The length of the base is 14√3 inches

The area of the triangle is 49√3 square inches

#SPJ2

For similar questions refer to:

https://brainly.in/question/38451