Math, asked by meero4093, 1 year ago

Two sides of a triangle are 50 m and 60 m long. the angle included between these sides is 30 deg. what is the interior angle opposite the longest side?

Answers

Answered by Aditijani1
0
B ki value hogi 86.38
Answered by SushmitaAhluwalia
0

Given:

The lengths of the two sides of a triangle are 50 m and 60 m

The value of the included angle is 30°.

To find:

The value of interior angle opposite to the longest side

Solution:

To solve this we will use the cosine rule or the law of cosines,

which states that the square of the third side of a triangle is the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Assuming,

A= 50 cm

B = 60 cm

∠C = 30°

c²=a²+b²-2abcosC.

Substituting the values

c²=(50)²+(60)²-2(50)(60)cos(30)

c = 30.06 m

According to this,  B which is equal to 60 cm is the longest side

Now let's find the angle opposite to this side, ∠C

Using the law of sines that states that the ratio of the side and the corresponding angle of a triangle is equal to the ratio of other sides and their corresponding angles.

A/sin∠A = B/sin∠B = C/sin∠C

B/sin∠B = C/sin∠C

substituting values

60/ sin∠B  = 30.06/sin (30°)

sin∠B = 60 × sin (30°) / 30.06

sin∠B = 60 ×  0.5 / 30.06

sin∠B = 30/ 30.06

If we approximate the

sin∠B = 1

∠B = 90°

But we if take precise value then the answer

sin∠B = 0.998

∠B = 86.38°

Therefore, the interior angle opposite the longest side is 86.38°.

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