Advertisements
Advertisements
प्रश्न
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
Advertisements
उत्तर
Here, we need to measure the distance AB as shown in the figure below,
Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
Therefore, in this case
AB2 = BC2 + CA2
AB2 = 502 + 402
AB2 = 2500 + 1600
AB2 = 4100
AB = 64.03
Therefore the required distance is 64.03 m.
APPEARS IN
संबंधित प्रश्न
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
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?
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2
In ∆ ABC, AD ⊥ BC.
Prove that AC2 = AB2 +BC2 − 2BC x BD
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
Find the Pythagorean triplet from among the following set of numbers.
3, 4, 5
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.
A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.
In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason
If ΔABC ~ ΔPQR, `("ar" triangle "ABC")/("ar" triangle "PQR") = 9/4` and AB = 18 cm, then the length of PQ is ______.
In a quadrilateral ABCD, ∠A + ∠D = 90°. Prove that AC2 + BD2 = AD2 + BC2
[Hint: Produce AB and DC to meet at E.]
Two angles are said to be ______, if they have equal measures.
If the areas of two circles are the same, they are congruent.
