Question

the three inside angles (A,B and C) of a right-angled triangle are in the ratio 7:18:11 the smallest angle is 35 degrees work out angles A,B and C

Answer 1

Answer:

Therefore the measure of the angles of a right angled triangle ABC are,

$\angle A=35\°\\\angle B= 90\°\\\angle C= 55\°$

Step-by-step explanation:

Let the Common multiple be  ' x '

given the angles are in the ratio 7 : 18 : 11

Therefore the angles are

∠A = 7x , ∠B = 18x  , ∠C = 11x

To Find:

∠A = ? , ∠B = ? , ∠C =?

Solution:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

$\angle A+\angle B+\angle C=180\°$   ..Triangle sum property.

Substituting the values we get

$7x+18x+11x=180\\36x=180\\x=\dfrac{180}{36}=5\\\\x=5$

substitute ' x ' in the measure angles we get

$\angle A=7\times 5= 35\°\\\angle B=18\times 5= 90\°\\\angle C=11\times 5= 55\°$

Therefore the measure of the angles of a right angled triangle ABC are,

$\angle A=35\°\\\angle B= 90\°\\\angle C= 55\°$