Answers
Answer:
a) root77
b) 2 root77 / ~17.55 cm^2
Step-by-step explanation:
a) by using Pythagorean Theroem,
a^2 + b^2 = c^2
2^2 + b^2 = 9^2
4 + b^2 = 81
81 - 4 = b^2
77 = b^2
root77 = b
b) 1/2bh is the quation for area thus,
area = 1/2 ( 4 ) ( root77)
area = 2 root77
or area = ~17.55 cm^2
h = [tex]\sqrt{77}[/tex]
A =[tex]2\sqrt{77}[/tex]
Step-by-step explanation:Rules for solving this problem:
Isosceles triangle rules
∠C = ∠ABC = BABecause of isosceles being made up of two right triangles; using the pythagorean theorem we can deduce that
(1/2 x AC)² = BC² - h² (1/2 x AC)² = BA² - h²Area of a triangle
A = 1/2 (Base x Height) = 1/2 * bhStep 1 - Find the height
[tex]h =\sqrt{9^2 - ((1/2)AC)^2} = \sqrt{9^2 - ((1/2)~4)^2} = \sqrt{9^2 - 2^2} = \sqrt{81-4} = \sqrt {77}[/tex]
Step 2 - Find the area
[tex]A = \frac{1}{2}bh = (\frac{1}{2})(4)(\sqrt{77}) = 2 \sqrt{77}[/tex]
Hope this helps,
- J.M.Jamon
Pennsylvania State University
Full-time B.S.CE. undergrad student
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