Jason found the measure of angle A

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Jason and Allison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of 22° 8’ 6”. At the same time, Allison is standing 48 feet closer to the tree, measuring an angle of elevation of 30° 40’ 30” to the owl. If Jason and Allison are the same height, their eyes 5 feet from the ground, find the height of owl in the tree.

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Type the correct answer in each box. If necessary, round your answers to the nearest hundredth.

disa [49]

Answer:

Perimeter = 32.44 units

Area = 30 square units

Step-by-step explanation:

Given

Vertices

A(2,8), B(16,2) and C(6,2)

WE have to determine the lengths of all sides before finding the perimeter and area.

The formula of modulus is:

$d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\$

So the perimeter is:

$Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units$

Using hero's formula,

$s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units$