Question

in right triangle abc, ( b^{2}+c^{2}=34 ) and ( bc = 15 ). what is the approximate length of side a?
note: use the law of cosines.
a. 6 units
b. 5 units
c. 3 units
d. 4 units

Explanation:

Step1: Recall the law of cosines

In a triangle, \(a^{2}=b^{2}+c^{2}-2bc\cos A\).

Step2: Substitute the given values

Given \(b^{2}+c^{2} = 34\), \(bc = 15\), and \(A = 53^{\circ}\) (\(\cos53^{\circ}\approx0.6\)).

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Step3: Solve for \(a\)

Take the square root of both sides: \(a=\sqrt{16}\).

Answer:

D. 4 units