Answer:
i. The ratio of the areas of the two triangles is 5:8.
ii. The area of the larger triangle is 24 in².
Step-by-step explanation:
Let the area of the smaller triangle be represented by
, and that of the larger triangle by
.
Area of a triangle =
x b x h
Where; b is its base and h the height.
Thus,
a. The ratio of the area of the two triangles is:

Area of smaller triangle =
x b x h
=
x 5 x h
=
h
Area of the lager triangle =
x b x h
=
x 8 x h
= 4h
So that;
Ratio = 
= 
The ratio of the areas of the two triangles is 5:8.
b. If the area of the smaller triangle is 15 in², then the area of the larger triangle can be determined as;
= 
= 
5
= 15 x 8
= 120
= 
= 24
The area of the larger triangle is 24 in².
Answer:
2 solutions
Step-by-step explanation:
Since the equations are not equal, they provide two solutions. Negative numbers provide no solutions. If they are equal to zero, they have one solution.
Length of x is 98.2 m
<u>Step-by-step explanation:</u>
Step 1:
Use the trigonometric ratio tan 27° to find the common side of both the right angled triangles.
tan 27° = opposite side/adjacent side = opposite side/9
∴ Opposite side = 9 tan 27° = 9 × - 3.27 = -29.46 m
Step 2:
Use this side and trigonometric ratio cosine to find the value of x.
cos 49° = adjacent side/x = -29.46/x
∴ x = -29.46/cos 49° = -29.46/0.30
= 98.2 m (negative value neglected)
Answer:
5(1/5^3) ≠ 5(5^3)
Step-by-step explanation:
5(1/5^3) = 5(5^3)
5/27 = 625
5(1/5^3) ≠ 5(5^3)
The sides aren't equal, so this equation is FALSE.