Watching from the top of a building 40 , m hi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $\overline{AB}$ be the building of height $40 \, m$. Let $C$ and $D$ be the two positions of the moving car.From the figure,$AB = 40 \, m$ and

Vedclass · Accepted Answer

$29.2$

Vedclass · Answer

(B) Let $\overline{AB}$ be the building of height $40 \, m$. Let $C$ and $D$ be the two positions of the moving car.From the figure,$AB = 40 \, m$ and $\angle B = 90^{\circ}$.The angles of depression are $\angle XAC = 45^{\circ}$ and $\angle XAD = 30^{\circ}$.Since the line $AX$ is parallel to $BD$,the alternate interior angles are equal:$\angle ACB = \angle XAC = 45^{\circ}$ and $\angle ADB = \angle XAD = 30^{\circ}$.In right-angled $	riangle ABC$:$	an(45^{\circ}) = \frac{AB}{BC} \implies 1 = \frac{40}{BC} \implies BC = 40 \, m$.In right-angled $	riangle ABD$:$	an(30^{\circ}) = \frac{AB}{BD} \implies \frac{1}{\sqrt{3}} = \frac{40}{BD} \implies BD = 40\sqrt{3} \, m$.Using $\sqrt{3} \approx 1.73$,we get $BD = 40 	imes 1.73 = 69.2 \, m$.The distance covered by the car is $CD = BD - BC$.$CD = 69.2 - 40 = 29.2 \, m$.Thus,the distance covered by the car is $29.2 \, m$.

Watching from the top of a building $40 \, m$ high,the angle of depression of a moving car increases from $30^{\circ}$ to $45^{\circ}$ in some interval of time. Find the distance covered by the car in that interval of time. (in $m$)

Similar Questions

The union of the horizontal ray and the ray of vision forms the angle of elevation; then the object under observation is $\ldots \ldots \ldots . .$

The height of a tower is $60 \, m$. From a point on the ground,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the distance of that point from the base of the tower. (in $m$)

The height of a building is $11 \, m$ and the height of a pole is $8 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the pole is $\alpha$ and that of the top of the building is $\beta$. Then,$\ldots \ldots \ldots$ holds true.

Find the angle of elevation of the sun when the shadow of a pole $h$ meters high is $\sqrt{3} h$ meters long. (in $^{\circ}$)

Two trucks are parked in the same direction of a $300 \,m$ high tower. The angles of depression of these trucks from the top of the tower are found to be $45^{\circ}$ and $60^{\circ}$. Find the distance between these two trucks. (in $,m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module