In triangle ABC, it is given that angle A is 59 degrees and angle B is 53 degrees. The altitude from B to line AC is extended un
til it intersects the line through A that is parallel to segment BC; they meet at K. Calculate the size of angle AKB.
2 answers:
Answer:
∠AKB = 22°
Step-by-step explanation:
Call the point of intersection of BK and AC point P. Then line BK is a transversal to parallel lines AK and BC. Alternate interior angles AKB and PBC will be congruent.
We know that angle PCB is 68°, the difference between 180° and the sum of the two given angles in ΔABC:
∠PCB = 180° -∠PAB -∠ABC = 180° -59° -53° = 68°
Since PB is an altitude, ∠CPB is a right angle. Then ∠PBC is the complement of ∠PCB, so is ...
∠PBC = 90° -68° = 22°
As we said, this is congruent to ∠AKB, so ...
∠AKB = 22°
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Answer:
The space inside the box = 2197 in³ - 1436.76 in³ is 760.245 in³.
Step-by-step explanation:
Here we have the volume of the cube box given by the following relation;
Volume of cube = Length. L × Breadth, B × Height, h
However, in a cube Length. L = Breadth, B = Height, h
Therefore, volume of cube = L×L×L = 13³ = 2197 in³
Volume of the basketball is given by the volume of a sphere as follows;
Volume =
Where:
r = Radius = Diameter/2 = 14/2 = 7in
∴ Volume of the basketball =
Therefore, the space inside the box that is not taken up by the basketball is found by subtracting the volume of the basketball from the volume of the cube box, thus;
The space inside the box = 2197 in³ - 1436.76 in³ = 760.245 in³.