Advertisements
Advertisements
प्रश्न
In Fig. 3, the area of triangle ABC (in sq. units) is:
पर्याय
(A) 15
(B) 10
(C) 7.5
(D) 2.5
उत्तर
Construction: Draw AM ⊥ BC.
It can be observed from the given figure that BC = 5 unit and AM = 3 unit.
In ΔABC, BC is the base and AM is the height.
∴ Area of triangle ABC = `1/2xx`base x height
`=1/2xxBCxxAM`
`=1/2xx5xx3` sq.units
=7.5 sq.units
APPEARS IN
संबंधित प्रश्न
A ladder makes an angle of 60° with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is:
(A) `4/sqrt3`
(B) `4sqrt3`
(C) `2sqrt2`
(D)4
Two stations due south of a leaning tower which leans towards the north are at distance a and b from its foot. If α, β be the elevations of the top of the tower from these stations, prove that its inclination θ to the horizontal is given by `\text{cot }\theta =\frac{bcot alpha -a\cot \beta }{b-a}`
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.
The length of the shadow of a tower standing on the level plane is found to 2x meter longer when the sun's altitude is 30° than when it was 45°. Prove that the height of the tower is `x(sqrt3 + 1)` meters.
A fire in a building B is reported on the telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. Which station should send its team and how much will this team have to travel?
A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point where the ladder touches the wall.
The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find (i) the difference between the heights of the light-house and the building. (ii) the distance between the light-house and the building.
The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°, then the distance between the two towers is ____________.
Read the following passage:
A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m.
|
Based on the above information, answer the following questions.
- What is the measure of ∠APD?
- If ∠YAQ = 30°, then ∠AQD is also 30°, Why?
- Find length of PD
OR
Find length of DQ
