Answer:
x-0.75x=9.00
-0.74x=9.00
x=0.74+9.00
x=9.74
Step-by-step explanation:
Given that the diagram shows the location of John and Mark in relationship to the top of the building labeled A, then:
a]
∠4 is the angle of elevation as seen by Mark from his location. It is the angle between the horizontal and the line from the object to the observer's eyes.
b]
∠3 is the angle of depression and it is congruent to the angle 5, which is the angle of elevation as seen by John from his location.
B because 5xanything ends in 0 or 5
Answer:
5 cm
Step-by-step explanation:
If AB is tangent to the circle k(O), then radius OB is perpendicular to segment AB.
If BC is tangent to the circle k(O), then radius OC is perpendicular to segment AC.
Consider two right triangles ABO and ACO. In these triangles:
- AO is common hypotenuse;
- ∠OBA=∠OCA=90°, because AB⊥OB, AC⊥OC;
- OB=OC as radii of the circle k(O).
By HL theorem, triangles ABO and ACO are congruent. Then
- ∠OAB=∠OAC=30°;
- AC=AB=5 cm.
Hence, ∠BAC=∠OAB+∠OAC=30°+30°=60°.
Consider triangle ABC, this triangle is isosceles triangle. In isosceles triangles angles adjacent to the base are congruent, thus
∠CBA=∠BCA=1/2(180°-60°)=60°.
Therefore, triangle ABC is an equilateral triangle, so BC=AB=AC=5 cm.