The shorter leg of a \( 30 ^ { \circ } - 60 ^ { \circ } - 90 ^ { \circ } \) triangle measures \( 4 \sqrt { 2 } \) kilometers. What is the measure of its hypotenuse?
A. \( 8 km \) .
B. \( 8 \sqrt { 2 } km \) .
C. \( 8 \sqrt { 3 } km \) .
D. \( 4 \sqrt { 6 } km \) .
Jason places a mirror on the ground \( 40 \) feet from the base of a tree. He walks backward until he can see the top of the tree in the middle of the mirror. At that point, Jason's eyes are \( 6 \) feet above the ground and he is \( 8 \) feet from the image in the mirror. Wha] is the height of the tree? A. \( 30 \) feet B. \( 32 \) feet C. \( 53 \) feet D. \( 46 \) feet
A. \( 30 \) feet
B. \( 32 \) feet
C. \( 53 \) feet
D. \( 46 \) feet
A \( 10 \) foot ladder is leaning against a building. The ladder makes a \( 45 \) degree angle with the building. How far up the building does the ladder reach?
A. \( 5 \sqrt { 2 } \) feet
B. \( 20 \sqrt { 2 } \) feet
C. \( 10 \sqrt { 2 } \) feet
D. \( 5 \) feet
