Question

Draw and label all three sides of a right triangle that has 40 degrees angle and a hypotenuse of 10cm

Answer 1

Answer:

Consider a right angle triangle ABC such that  B =90 degree as shown in figure given below with all the three sides labelled.

let $\angle C = 40^{\circ}$

Sum of all the measures of an angle in a triangle is 180 degree.

In triangle ABC

$\angle A +\angle B +\angle C =180^{\circ}$

$40^{\circ}+90^{\circ}+\angle C= 180^{\circ}$

or

$130^{\circ}+\angle C= 180^{\circ}$

Simplify:

$\angle C= 50^{\circ}$

The side AC (Hypotenuse) = 10 cm

Now, find the other sides i.e, AB and BC;

Using Sine rule

In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse side.

then

$\sin B = \frac{opposite side}{Hypotenuse side} =\frac{AB}{AC}$

or

$\sin 40^{\circ} = \frac{AB}{10}$

or

$AB =10 \times \sin 40^{\circ}$

Simplify:

AB = 6.4278761 ≈ 6.43 cm

Now,by using tangent rule to solve for BC

In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.

then;

$\tan B = \frac{opposite side}{Adjacent side} =\frac{AB}{BC}$

or

$\tan 40^{\circ} = \frac{6.4278761}{BC}$

or

$BC =\frac{6.4278761}{\tan 40^{\circ}}$

Simplify:

BC = 7.66044443≈ 7.66 cm

therefore, the sides AB and BC of the triangle ABC are 6.43(approx) and 7.66(approx.)