Advertisements
Advertisements
Question
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
Options
True
False
Solution
This statement is True.
Explanation:
sec A = `12/5`
`"Hypotenuse"/"Side adjacent to ∠A" - 12/5`
`("AC")/("AB") = (12/5)`
Let AC be 12k, AB will be 5k, where k is a positive integer.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(12k)2 = (5k)2 + BC2
144k2 = 25k2 + BC2
BC2 = 119k2
BC = 10.9k
It can be observed that for given two sides AC = 12k and AB = 5k,
BC should be such that,
AC − AB < BC < AC + AB
12k − 5k < BC < 12k + 5k
7k < BC < 17 k
However, BC = 10.9k
Clearly, such a triangle is possible and hence, such value of sec A is possible.
Hence, the given statement is true.
APPEARS IN
RELATED QUESTIONS
Given sec θ = `13/12`, calculate all other trigonometric ratios.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
sin (45° + θ) – cos (45° – θ) is equal to ______.
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to ______.
If sin A = `1/2`, then the value of cot A is ______.
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.
The value of the expression (sin 80° – cos 80°) is negative.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
