Mis the midpoint of JK. JM = x + 1 and JK = 20. Find the value
of x and MK.

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Ответ:

mrmendrala

16.06.2020

Mathematics

15 meters

Step-by-step explanation:

Denote points: C - cat, B - base of the tree, D - dog, F - Firefighter.

Consider triangle CBD. This triangle is right triangle with right angle CBD and m∠BCD=65°, DB=10 m. Then

$\dfrac{BC}{BD}=\tan 65^{\circ},\\ \\BC=BD\cdot \tan 65^{\circ}\approx 10\cdot 2.14=21.4\ m.$

Consider right triangle CBF. In this triangle angle CBF is right angle and m∠CFB=50°, then

$\dfrac{BC}{BF}=\tan 50^{\circ},\\ \\BF=\dfrac{BC}{\tan 50^{\circ}}\approx \dfrac{21.4}{1.91}\approx 11.2\ m.$

Consider right triangle BDF. In this triangle angle FBD is right and by the Pythagorean theorem,

$DF^2=BF^2+BD^2,\\ \\DF^2=(11.2)^2+10^2,\\ \\DF^2=225.44,\\ \\DF\approx 15\ m.$

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Mis the midpoint of JK. JM = x + 1 and JK = 20. Find the value of x and MK.