Answer:
8.06
Step-by-step explanation:
We can find the length of AB using the principle of similar triangles on the triangles ABD and ABC. We would also engage the use of trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,
SOA stands for
Sin Ф = opposite side/hypotenuses side
Cosine Ф = adjacent side/hypotenuses side
Tangent Ф = opposite side/adjacent side
Considering triangle ABD, given that AD = 5 then
Cos A = AD/AB
Also,
Cos A = AB/AC
Given that AD = 5, AC = 13, AB = x
therefore,
x/13 = 5/x
x² = 65
x = √65
= 8.06
Answer:
[tex]AB = \sqrt{\frac{121}{2} }[/tex]
Step-by-step explanation:
Here we have
AD = 5 = a
AC = 13 = c
∴ BC = 13 - 5 = 8
BD = x = √(AB² + BD²) = √(16 + BD²)
8² + BD² = BC² → BC² - BD² = 64 .......................(1)
13² - x² = BC² → BC² + x² = 169.........................(2)
x² = 16 + BD² → x² - BD² = 16.............................(3)
Solving the three equations with three unknowns by subtracting equation (3) from (2) we have;
BC² + BD² = 153...............................................................(4)
Adding equation foru to one give
2BC² = 217
∴ BC² = 217/2
Similarly, BD² = 89/2 and
x² = 121/2
Therefore, x = AB = √(121/2).
