Answer:
5 ; 12 ; 13
Step-by-step explanation:
Let :
Shorter leg = x
Other leg = x + 7
Hypotenus = x + 8
Recall:
Hypotenus² = opposite² + adjacent²
(x+8)² = x² + (x+7)²
x² + 16x + 64 = x² + x² + 14x + 49
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x(x - 5) +3(x - 5) = 0
(x + 3) = 0 ; x = - 3
(x - 5) = 0 ; x = 5
Side can't be negative ;
Hence,
x = shorter side = 5
Other side = x + 7 = 5 + 7 = 12
Hypotenus = x + 8 = 5 + 8 = 13
Answer:
The expression which doesn't belong to the other three is (-34 + 58).
Step-by-step explanation:
Given:
Four expressions.
We have to find the odd one out.
The expressions are :
We know that with same signs (operator) in addition/subtraction of an expression we we add the values and the answer remains in negative.
But with different signs on numbers we will subtract the numbers and the greater number's sign will be carried forward.
So,
We can see that the second expression is not equal to the other three.
(-34 + 58) is the odd one out of the four expressions.
Answer:
The angle formed between CF and the plane ABCD is approximately 47.14°
Step-by-step explanation:
The given parameters are;
BC = 6.8
DE = 9.3
∠BAC = 52°
We note that the angles formed by the vertex of a cuboid are right triangles, therefore, by trigonometric ratios, we get;
sin∠BAC = BC/(The length of a line drawn from A to C)
∴ The length of the line drawn from A to C = BC/sin∠BAC
The length of the line drawn from A to C = 6.8/sin(52°) ≈ 8.63
∴ AC = 8.63
By trigonometry, we have;
The angle formed between CF and the plane ABCD = Angle ∠ACF


In a cuboid, FA = BG = CH = DE = 9.3


The angle formed between CF and the plane ABCD = Angle ∠ACF ≈ 47.14°