UPCAT & Civil Service (Philippines) · Mathematics & Science Proficiency

Trigonometry and Spatial Word Problems

6 practice questions, each with the answer and an explanation.

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From the top of a lighthouse 60 meters above sea level, the angle of depression of a boat is $3 0^{\circ}$ . How far is the boat from the base of the lighthouse?
Simplify the trigonometric expression: $\frac{s i n ( 2 θ )}{1 + c o s ( 2 θ )}$ .
A triangular plot of land has two adjacent sides measuring $8 m$ and $10 m$ , forming an included angle of $12 0^{\circ}$ . What is the area of this land?
A solid right circular cone has a base radius of $6 cm$ and a slant height of $10 cm$ . What is the volume of this cone?
If $tan (θ) = - \frac{3}{4}$ and $θ$ is in Quadrant II, what is the exact value of $cos (θ)$ ?
What is the length of side $c$ in $△ A B C$ if $a = 7$ , $b = 5$ , and $∠ C = 6 0^{\circ}$ ?

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