Question 11
In triangles PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is ΔQPR~ΔTSM?
Why?
Solution
We know that the sum of three angles of a triangle is 180°.
In ΔPQR, ∠P + ∠Q + ∠R = 180°
⇒ 55° + 25° + ∠R = 180°
⇒ ∠R = 180° – (55° + 25°)= 180° – 80° =100°
In ΔTSM, ∠T + ∠S + ∠M = 180°
⇒ ∠T + ∠25°+ 100° = 180°
⇒ ∠T = 180°-(25° +100°)
=180°-125°= 55°
In ΔPQR and A TSM, and
∠P = ∠T, ∠Q = ∠S and ∠R = ∠M
ΔPQR ~ ΔTSM [since all corresponding angles are equal]
Hence, ΔQPR is not similar to ΔTSM, since the correct correspondence is P ↔ T, Q <
r→ S and R ↔M
Question 12
Determine the length of an altitude of an equilateral triangle of side ‘2a’ cm
Solution
Applying Pythagoras theorem
AD= √3 a cm
Question 13
A boy of height 80 cm is walking away from the base of a lamp-post at a
speed of 1.1 m/s. If the lamp is 3.2 m above the ground, find the length of
her shadow after 3 seconds.
Solution
DE= 1.1 m
Question 14
Arjun is 5 feet tall. He places a mirror on the ground and moves until he can see the top of a tower. At the instant when Arjun is 3 feet from the mirror, the tower is 54 feet from the mirror. How tall is the tower?
Solution
h = 72 𝑚𝑒𝑡𝑒𝑟
Question 15
A vertical pole of length 8 m casts a shadow 6 cm long on the ground and at the same time a tower casts a shadow 30 m long. Find the height of tower.
Solution
∴ EF = 40 m
SELF ASSESSMENT
Q1. In the backyard of house, Shikha has some empty space in the shape of a
ΔPQR. She decided to make it a garden. She divided the whole space into three
parts by making boundaries AB and CD using bricks to grow flowers and
vegetables where AB II CD II OR as shown in figure. Find the length of AB and
CD also find area of Δ PAB.
Q2. A vertical pole of length 8 m casts a shadow 6 cm long on the ground and at
the same time a tower casts a shadow 30 m long. Find the height of tower.
Q3. It is given that ∆ABC and ∆EDF are similar such that AB = 5 cm, AC = 7 cm, DF= 15 cm
and DE = 12 cm. Find the lengths of the remaining sides of the triangles.
Q4. A street light bulb is fixed on a pole 6 m above the level of street. If a woman of
height 1.5 m casts a shadow of 3 m, find how far she is away from the base of
the pole?
