jonestheproblem5029
09.03.2020 •
Mathematics
There is a triangle with measures of 5, 12, 14. Is this a right triangle? Why or why not?
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Ответ:
no,it isnt,
Step-by-step explanation:
pythagoras property of right angle:
height sq + base square = hypotenuse sq
5*2+12*2=14*2
25+144=196 which is wrong
Ответ:
D = 32°
E = 102°
F = 46°
Step-by-step explanation:
The measure of angle D is 14 less than the measure of angle F
⇒ D = F - 14
The measure of angle E is 10 more than twice the measure of angle F:
⇒ E = 2F + 10
So we have now constructed two equations:
Equation 1: D = F - 14
Equation 2: E = 2F + 10
Also, we know that the sum of the interior angles of a triangle is 180°.
Therefore, D + E + F = 180
Substitute the two equations we have constructed for D and E into the sum of the interior angles equation and solve for F
D + E + F = 180
⇒ (F - 14) + (2F + 10) + F = 180
⇒ 4F - 4 = 180
⇒ 4F = 180 + 4 = 184
⇒ F = 184 ÷ 4
⇒ F = 46°
Now substitute the found value of angle F into the two equations for D and E:
D = F - 14
⇒ D = 46 - 14
⇒ D = 32°
E = 2F + 10
⇒ E = 2(46) + 10
⇒ E = 92 + 10
⇒ E = 102°