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Can anyone help to solve this for my brother?

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I am not familiar with the way question 12 is worded, but I think you are supposed to use similarity of triangles to find the lengths of XY and YZ, which are half the lengths of AB and BC, respectively.

For the first question, it is important to remember that diagrams are not to scale.  Since angles A measures 45 degrees and h is an altitude, intersecting AB at a 90 degree angle, angle AC(unnamed point where h intersects AB) is also 45 degrees.  That makes the small triangle isosceles right triangle and h is the same length as 1/2 of AB.  Use the Pythgorean Theorem or propetries of special right triangles to find the length of AC.
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altitude h is always perpendicular to AB. You can use congruency of triangles to prove that the point at which the altitude meets AB (say D) is the midpoint of AB. I mean ASA congruency is super easy to notice. Or even Right angle congruency.   
Anyway once you’ve done that use tan 45 = 1 to find out h. And either pythagoras’ theorem for AC or any of the other trig ratios leaving out tan and cot.

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