Advertisements
Advertisements
प्रश्न
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `5sqrt(2)`, then what is the height of ∆ABC?
Advertisements
उत्तर
AB = BC ...[Given]
∴ ∠A = ∠C ...[Isosceles triangle theorem]
Let ∠A = ∠C = x ...(i)
In ∆ABC, ∠A + ∠B + ∠C = 180° ...[Sum of the measures of the angles of a triangle is 180°]
∴ x + 90° + x = 180° ...[From (i)]
∴ 2x = 90°
∴ x = `90^circ/2`
∴ x = 45°
∴ ∠A = ∠C = 45°
∴ ∆ABC is a 45° – 45° – 90° triangle.
∴ AB = BC = `1/sqrt(2) xx AC` ...[Side opposite to 45°]
= `1/sqrt(2) xx 5sqrt(2)`
∴ AB = BC = 5 units
∴ The height of ∆ABC is 5 units.
APPEARS IN
संबंधित प्रश्न
If the sides of a triangle are 3 cm, 4 cm, and 6 cm long, determine whether the triangle is a right-angled triangle.
In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.
Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
In a ΔABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that
(i) AD = a`sqrt3`
(ii) Area (ΔABC) = `sqrt3` a2
In an acute-angled triangle, express a median in terms of its sides.
In ∆ABC, ∠A is obtuse, PB ⊥ AC and QC ⊥ AB. Prove that:
(i) AB ✕ AQ = AC ✕ AP
(ii) BC2 = (AC ✕ CP + AB ✕ BQ)
In a quadrilateral ABCD, ∠B = 90°, AD2 = AB2 + BC2 + CD2, prove that ∠ACD = 90°.
∆ABD is a right triangle right-angled at A and AC ⊥ BD. Show that
(i) AB2 = BC × BD
(ii) AC2 = BC × DC
(iii) AD2 = BD × CD
(iv) `(AB^2)/(AC^2) = (BD)/(DC)`
Determine whether the triangle having sides (a – 1) cm, `2sqrta` cm and (a + 1) cm is a right-angled triangle.
State the converse of Pythagoras' theorem.
If D, E, F are the respectively the midpoints of sides BC, CA and AB of ΔABC. Find the ratio of the areas of ΔDEF and ΔABC.
Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.
A man goes 12 m due south and then 35 m due west. How far is he from the starting point?
From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then `l` (AB) = ?
Find the altitude of an equilateral triangle of side 8 cm.
