# Determine the value of x to the nearest tenth of a centimeter?

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May 10, 2017

x=68.2377 nearest tenth of a centimeter is 68.2 cms

#### Explanation:

First consider the Right triangle ABC. BC= x sin 27

Next consider triangle DBC. Side DB=DC=27 (given). Now apply the cosine rule

Cos D=Cos 70=$\frac{D {B}^{2} + D {C}^{2} - B {C}^{2}}{2 B D \cdot D C}$

$\cos 70 = \frac{{27}^{2} + {27}^{2} - B {C}^{2}}{2 \cdot 27 \cdot 27}$

$1458 \cos 70 = 729 + 729 - B {C}^{2}$

$B {C}^{2} = 1458 - 1458 \cos 70$

${\left(0. 4539 x\right)}^{2} = 1458 - 1458 \left(0.34202\right)$

$$                     =959.3346


0.4539x= 30.9731

x= 68. 2377

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