Question

In an isosceles triangle the equal sides are 12m. Solve it knowing that there are two 70 ° angles .

Help me please :(

Answer 1

Answer:

In an isosceles right triangle, the equal sides make the right angle. They have the ratio of equality, 1 : 1. To find the ratio number of the hypotenuse h, we have, according to the Pythagorean theorem, h2 = 12 + 12 = 2.

Answer 2

Answer:

The unknown angle = 40°

The unknown side = 8.313m

Step-by-step explanation:

GIVEN :-

• The Two equal sides of the isosceles triangle = 12m
• The equal angles of the isosceles triangle = 70°

TO FIND :-

• The third side and angle of the isosceles triangle

SOLUTION :-

STEP I

(Finding the third angle)

We know that,

The sum of all angles in a triangle = 180°

Let the third unknown angle of this triangle be x

=> 70 + 70 + x = 180

=> 140 + x = 180

=> x = 180 - 140

=> x = 40

Therefore, the third angle of the isosceles triangle is 40°

STEP II

(Finding the third side)

For this step we'll be applying The Law of Cosines according to which:-

If the length of two sides and the angle between them is known for a triangle, then we can determine the length of the third side, using the given formula -

a² = b² + c² - 2bc cos(A)

• a is the third unknown side
• b and c are the known sides
• A is the angle between b and c

Solving further...

Taking,

1. b and c = 12 m
2. A = 40

So, the third side ,a, will be calculated as:-

=> a²= (12)² + (12)² - (2 × 12 × 12 × cos40)

=> a² = 144 + 144 - 288 cos40

=> a² = 288 (1 - cos40)

=> a² = 288 (1 - 0.76)

=> a = $\sqrt{288 \:(0.24)}$

=> a = $\sqrt{69. 12}$

=> a = 8.313

Therefore, the third side of the isosceles triangle is 8.313 m

                                     

Hope this helps!