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From point $A$ the angle of elevation to the top of a newly constructed building is $17.2$ deg. From point $B$ which is $153$ meters closer to the building the angle of elevation at the top of the building is $25$ deg. Solve the triangle.

smaller triangle: $\angle B = 155^\circ\,; \angle C = 7.8^\circ\,; b = 476.4\mathrm{m}\,; a = 333.3\mathrm{m}$

bigger triangle: $\angle C = 65^\circ\,; a = 333.3 \times h\,;b = 140.9\mathrm{m}\,; c = 302.2\mathrm{m}$

Height = $140.9 \mathrm{m}$ ????

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actually in this type of question mostly height asked.so are you asking the height or anything else? –  iostream007 May 17 '13 at 16:46

1 Answer 1

Let the base of the smaller triangle be $b$. Then the base of the bigger triangle is $b+153$. Let the height of the building be $h$. Then we have $$\frac{h}{b}=\tan(25^\circ); \quad \frac{h}{b+153}=\tan(17.2^\circ).$$ It follows that $$b\tan(25^\circ)=(b+153)\tan(17.2^\circ).$$ It follows that $$b=\frac{153\tan(17.2^\circ)}{\tan(25^\circ) -\tan(17.2^\circ)}.$$ The calculator gives that $b\approx 302.1347$. It follows that the height $b\tan(25^\circ)$ is approximately $140.8877$. These numbers are consistent with numbers that you obtained.

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