Answer:
Area of triangle is 25.
Step-by-step explanation:
We have been given an isosceles right triangle
Isosceles triangle is the triangle having two sides equal.
Figure is shown in attachment
By Pythagoras theorem
AD is altitude which divides the triangle into two parts
DC=5 implies BC =10 since D equally divides BC
Let AC=a implies AB=a being Isosceles
On substituting the values in the Pythagoras theorem:
WE can find area of right triangle by considering height AB and AD
Area of triangle ABC is:
(1)
And other method of area of triangle is:
(2)
Equating (1) and (2) we get:
Using area of triangle is:
Now, the area of triangle ABC=
From the trigonometry:
tan θ = (sin θ) / (cos θ)
cot θ = (cos θ) / (sin θ)
∴ tan θ + cot θ = (sin θ) / (cos θ) + (cos θ) / (sin θ)
= [ sin² θ + cos² θ]/( sin θ cos θ) = 1 /( sin θ cos θ )
note : sin² θ + cos² θ = 1
<span>9a + -3(2a + -4) = 15
Reorder the terms:
9a + -3(-4 + 2a) = 15
9a + (-4 * -3 + 2a * -3) = 15
9a + (12 + -6a) = 15
Reorder the terms:
12 + 9a + -6a = 15
Combine like terms: 9a + -6a = 3a
12 + 3a = 15
Solving
12 + 3a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 3a = 15 + -12
Combine like terms: 12 + -12 = 0
0 + 3a = 15 + -12
3a = 15 + -12
Combine like terms: 15 + -12 = 3
3a = 3
Divide each side by '3'.
a = 1
Simplifying
a = 1</span>
