on an algebra test, the highest grade was 42 points higher than the lowest grade. the sum of the two grades was 138. find the lo
2 answers:
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These are right triangles that will use either sin, cos, or tan, depending upon what you have to work with in regards to the reference angle. The first one has a reference angle of 51 with y being the side opposite it and 12 being the hypotenuse. The sin identity uses the side opposite over the hypotenuse as its formula:
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
and
and
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
and
and
with x = 29.238
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
and
and
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.
In the given diagram, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF. So the measure of angles are :
1. m∠DEF= 112° because ∠ABC≅∠DEF
2. m∠ABG= 56° because a straight line BG is bisecting ∠ABC in two equal parts. So,
3. m∠CBG= 56° because ∠ABG and ∠CBG are equal.
4. m∠DEG= 56° because ∠ABG ≅ ∠DEG