Advertisements
Advertisements
Question
In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.
Advertisements
Solution
In ΔABC, ∠B = 90°
∴ AC2 = AB2 + BC2 ....(Pythagoras Theorem)
⇒ 102 = AB2 + 62
⇒ AB2 = 102 - 62
= 100 - 36
= 64
Now,
BD = BC + CD
= 6 + 9
= 15cm
⇒ BD2 = 225
In ΔABD, ∠B = 90°
∴ AD2 = AB2 + BD2
⇒ AD2 = 64 + 225 = 289
⇒ AD = 17cm.
APPEARS IN
RELATED QUESTIONS
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?
In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.
Find the Pythagorean triplet from among the following set of numbers.
9, 40, 41
A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.
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 a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?
In a right angled triangle, the hypotenuse is the greatest side
Find the length of the support cable required to support the tower with the floor
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
In the figure, find AR
From given figure, In ∆ABC, If AC = 12 cm, then AB = ?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle.
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
