To find the value of \(\sec B\) in the given right-angled triangle, we need to first understand the trigonometric properties of the triangle.
In a right-angled triangle:
- The side opposite the right angle is the hypotenuse.
- The sides forming the right angle are the adjacent and opposite sides, relative to the angle being considered.
Given:
- The triangle is right-angled at \(A\).
- \(BC = 5.2\, \text{cm}\) (this is the hypotenuse, since it is opposite the right angle at \(A\)).
- \(AB = 3\, \text{cm}\) (this is one of the sides adjacent to angle \(B\)).
We need to find \(\sec B\), which is defined as:
\(\sec B = \frac{\text{Hypotenuse}}{\text{Adjacent side to } B} = \frac{BC}{AB}\)
Substituting the known values:
\(\sec B = \frac{5.2}{3}\)
Calculating this gives:
\(\sec B = 1.7333\ldots\)
Rounding this to two decimal places, we find:
\(\sec B \approx 1.73\)
Therefore, the correct answer is 1.73.
This calculation matches the option 1.73, confirming it is correct.
Similar Questions
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Important Questions from Trigonometric Ratios
If \(cosec~\theta =\frac{29}{21}\) where 0 < θ < 90°, then what is the value of 4 sec θ + 4 tan θ?
The value of \(\cot \left( {cose{c^{ - 1}}\frac{5}{3} + {{\tan }^{ - 1}}\frac{2}{3}\;} \right)\)
The distance of the highest point on the graph of the function y = √3 cos x + sin x from the x-axis is:
If A = π / 6 and B = π / 3, then consider the following statements:
I. sin A + sin B = cos A + cos B
II. tan A + tan B = cot A + cot B
Which of the above statements is / are correct?
If \(\sin A = \frac{1}{{\sqrt 2 }}\) and \({\mathop{\rm Cos}\nolimits} B = \frac{{\sqrt 3 }}{2}\), then, find the value of (A + B)º.
A. 60º
B. 75º
C. 105º
D. 90º
