Answer:
D
Step-by-step explanation:
The hypotenuse squared is equal to the sum of the legs squared in a right triangle.
∴ c² = a² + b² (Pythagorean’s Theorem)
c² = 3.4² + 6.7² (substitute the given values for a & b)
c² = 11.56 + 44.89 (square both right hand terms)
c² = 56.45 (add the right hand side values)
c = √56.45 (square root of both sides)
c ≈ 7.5 to the nearest tenth QED
Important:
The sum of the three angles inside
every triangle is always 180°.
First, look at the left triangle alone.
Two of its angles are 46° and 58° . (46° + 58° ) = 104°
That leaves (180° - 104° ) = 76° degrees for the third angle.
The third angle in that triangle is 'x'.
x = 76° .
At the point where 'x' and 'z' come together:
'x' and 'z' are a "linear pair".
Placed side-by-side, they form a straight line.
So (x + z) = 180° .
But x = 76°.
So z = (180° - 76°). z = 104° .
Now look at the the skinny triangle on the right alone.
The angle at the top is 13°, and z = 104°.
(13° + 104°) = 117° .
That leaves (180° - 117°) = 63° for the third angle.
'y' is the third angle.
y = 63° .
