What is \cos A + \cos B + \cos C equal to ?
Consider the following for the next three (03) items that follow : ABC is a triangular plot with AB=16\text{ m}, BC = 10\text{ m} and CA=10\text{ m}. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45^{\circ} at the vertex B.
- A. 1
- B. \frac{41}{25}
- C. \frac{37}{25}
- D. \frac{33}{25} ✓
Correct Answer: D. \frac{33}{25}
Explanation
Since a=10 and b=10, the triangle is isosceles and \cos A = \cos B. Using the cosine rule: \cos A = \frac{10^2+16^2-10^2}{2(10)(16)} = \frac{256}{320} = \frac{4}{5}. Thus, \cos B = \frac{4}{5}. For C: \cos C = \frac{10^2+10^2-16^2}{2(10)(10)} = \frac{200-256}{200} = -\frac{56}{200} = -\frac{7}{25}. The sum is \frac{4}{5} + \frac{4}{5} - \frac{7}{25} = \frac{40}{25} - \frac{7}{25} = \frac{33}{25}.
Related questions on Trigonometry
- What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm?
- What is the height of the lamp post?
- What is \frac{AB}{\sin C} equal to ?
- At what height is the top of the tower above the ground level?
- If \theta is the inclination of the tower to the horizontal, then what is \cot\theta equal to?