Given, a ladder 10 m long reaches a window 8 m above the ground.
Let BA be the wall and AC be the ladder,
Therefore, by Pythagoras theorem,
$AC^2 = AB^2 + BC^2$
$10^2 = 8^2 + BC^2$
$BC^2$ = 100 – 64
$BC^2$ = 36
BC = 6m
Therefore, the distance of the foot of the ladder from the base of the wall is 6 m.
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A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut? |
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An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of1200 km per hour. How far apart will be the two planes after $1\dfrac{1}{2}$ hours? |
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Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops. |
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D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $AE^2 + BD^2 = AB^2 + DE^2$. |
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The perpendicular from A on side BC of a Δ ABC intersects BC at D such that DB = 3 CD (see Fig. 6.55). Prove that $2 AB^2 = 2 AC^2 + BC2$ |  |
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In an equilateral triangle ABC, D is a point on side BC such that BD = $\dfrac{1}{3BC}$. Prove that $9 AD^2 = 7 AB^2$. |
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In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes. |
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Tick the correct answer and justify : In Δ ABC, AB = 6 3 cm, AC = 12 cm and BC = 6 cm. The angle B is : |
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Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 cm, 12 cm, 5 cm |
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PQR is a triangle right angled at P and M is a point on QR such that PM $\perp$ QR. Show that $PM^2$ = QM . MR. |
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