Question

In triangle abc the measure of angle b is thrice to the measure of angle c and the measure of angle a is half the sum of the measures of the angle b and angle

c.Find the measures of all the angles of triangle abc and also state the type of this triangle

Answer 1

Given:

There is a triangle.

∠B is thrice the measure of ∠C

∠A is half the sum of ∠B and ∠C

To FInd:

(1) The measure of each angle

(2) State the type of triangle

Solution

Define x:

Let ∠C be x

Find the angles in term of x:

∠C = x

∠B = 3x

∠A = 1/2 (3x + x)

Solve x:

Sum of angles in a triangle is 180

x + 3x + 1/2 (3x + x) = 180

x + 3x + 2x = 180

6x = 180

x = 30

Find the angles:

∠C = x

∠C = 30°

∠B = 3x

∠B = 3 x 30

∠B = 90°

∠A = 1/2 (x + 3x)

∠A = 1/2 (30 + 90)

∠A = 1/2 (120)

∠A = 60°

State the type of triangle:

The angles are 30°, 60° and 90°.

This triangle is known as a special right-angled triangle

Answers: The angles are 30°, 60° and 90°. It is a special right-angled triangle.

Answer 2

Answer:

An employee deposits certain amount at the rate of 8 % per annum and certain amount at the rate of 6 % per annum

at simple interest . He earns Rs 500 as annual interest . If he interchanges the amount at the same rates , he earns Rs 50

more . Find the amounts deposited by him at different rates .While arranging certain students of a school in rows containing equal number of student ; if three rows are

reduced , then three more students have to be arranged in each of the remaining rows . If three more rows are formed ,

then two students have to be taken off from each previously arranged rows .Find the number of student arranged .

(7)

4

5 3 15

x y

 

,

7

2 9 18

x y

 