Question

Q.2(A) Angle 1 ? 1 poin There are two levels of parking lot in a mall. A ramp rises to connect the two horizontal levels of parking i.e, level 1 to level 2. The ramp makes an angle of12° with the horizontal of level1.What is the measure of A) Anglei B) If the ramp makes an angle of 30 with the horizontal what will be the measurement of angle 1 level 2 1 Level 1


(a)168 degree

(b)178 degree

(c)182 degree​

Answer 1

Given:

Angle made by the ramp between level 1 and level 2 = 12°

To find:

Measure of ∠1.

If the ramp makes an angle of 30°, the measure of ∠1.

Solution:

From the figure, it can be seen that Level 1 and Level 2 are separated by a ramp and it is given that they are horizontal levels. Hence, the ramp acts as a hypotenuse of a right-angled triangle where level 1 is the base and level 2 is at the top of point A which is shown as a dotted line in the figure.

(a) Consider the right triangle BAC where the ramp angle is given as 12°. We need to find the measure of ∠1 or ∠C.

By angle sum property of a triangle,

$\angle A+\angle B +\angle C=180$

$90+12+\angle C=180$

$102+\angle C=180$

$\angle C=180-102=78^{0}$

(b) If the ramp angle is 30°, then the measure of ∠C is given by:

$\angle A+\angle B +\angle C=180$

$90+30+\angle C=180$

$120+ \angle C=180$

$\angle C=180-120=60^{0}$

If the angle made by the ramp is 12° with the horizontal, then the angle made between Level 1 and Level 2 is 78° and if the ramp makes 30° with the horizontal, then the angle made between Level 1 and Level 2 is 60°.