Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.
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A vertical building of height 59 m stands on level ground. Two observers, A and B, stand on the same side of the building on level ground. Observer A sees the top of the building at an angle of elevation of 36° and observer B sees the top at an angle of elevation of 66°. Find the distance between the two observers, correct to 1 decimal place.
Show the worked solution
Let $d_A$ m be the distance of observer $A$ from the building and $d_B$ m be the distance of observer $B$.
For observer $A$:
$\tan 36° = \dfrac{59}{d_A} \quad \scriptsize\textit{angle of elevation}$
$d_A = \dfrac{59}{\tan 36°}$
$d_A = \dfrac{59}{0.7265}$
$d_A = 81.21$ m (to 2 d.p.)
For observer $B$:
$\tan 66° = \dfrac{59}{d_B}$
Answer: 54.9
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Which syllabus does this follow?
O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.
Will it just show my child the answer?
No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.