Advertisements
Advertisements
Question
If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC =7units, find ∠B, AB and AC.
Advertisements
Solution
∠C = 90°, ∠A = 45°
∠A + ∠B + ∠C = 180°
45° + ∠B + 90° = 180°
∠B = 180° - 135°
∠= 45°
sin45° = `"BC"/"AB"`
⇒ AB = `"BC"/"sin45°"`
⇒ AB = `(7)/(1/sqrt(2)`
⇒ AB = `7sqrt(2)"units"`
Also,
tan45° = `"BC"/"AC"`
⇒ AC = `"BC"/tan45°"`
⇒ AC = `(7)/(1)`
⇒ AC = 7units.
APPEARS IN
RELATED QUESTIONS
If 2 cos 2A = `sqrt3` and A is acute,
find:
(i) A
(ii) sin 3A
(iii) sin2 (75° - A) + cos2 (45° +A)
State for any acute angle θ whether cos θ increases or decreases as θ increases.
Solve the following equation for A, if tan 3 A = 1
Solve the following equation for A, if 2 sin 3 A = 1
Calculate the value of A, if (cosec 2A - 2) (cot 3A - 1) = 0
Find the magnitude of angle A, if 2 cos2 A - 3 cos A + 1 = 0
Solve for x : sin2 60° + cos2 (3x- 9°) = 1
If `sqrt(3)` sec 2θ = 2 and θ< 90°, find the value of
cos2 (30° + θ) + sin2 (45° - θ)
In a rectangle ABCD, AB = 20cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.
If sec2θ = cosec3θ, find the value of θ if it is known that both 2θ and 3θ are acute angles.
